WORST_CASE(Omega(n^1),?)
proof of input_z1QKbSqJZe.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


The Runtime Complexity (parallel-innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).

(0) CpxRelTRS
(1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 410 ms]
(2) CpxRelTRS
(3) CpxTrsToCdtProof [BOTH BOUNDS(ID, ID), 94 ms]
(4) CdtProblem
(5) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxRelTRS
(9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
(10) typed CpxTrs
(11) OrderProof [LOWER BOUND(ID), 52 ms]
(12) typed CpxTrs
(13) RewriteLemmaProof [LOWER BOUND(ID), 324 ms]
(14) typed CpxTrs
(15) RewriteLemmaProof [LOWER BOUND(ID), 1833 ms]
(16) BEST
    (17) proven lower bound
        (18) LowerBoundPropagationProof [FINISHED, 0 ms]
        (19) BOUNDS(n^1, INF)
    (20) typed CpxTrs
        (21) RewriteLemmaProof [LOWER BOUND(ID), 1682 ms]
        (22) typed CpxTrs
        (23) RewriteLemmaProof [LOWER BOUND(ID), 1618 ms]
        (24) typed CpxTrs
        (25) RewriteLemmaProof [LOWER BOUND(ID), 24.3 s]
        (26) typed CpxTrs
        (27) RewriteLemmaProof [LOWER BOUND(ID), 23.7 s]
        (28) typed CpxTrs
        (29) RewriteLemmaProof [LOWER BOUND(ID), 24.2 s]
        (30) typed CpxTrs
        (31) RewriteLemmaProof [LOWER BOUND(ID), 5438 ms]
        (32) typed CpxTrs
        (33) RewriteLemmaProof [LOWER BOUND(ID), 502 ms]
        (34) typed CpxTrs
        (35) RewriteLemmaProof [LOWER BOUND(ID), 484 ms]
        (36) typed CpxTrs
        (37) RewriteLemmaProof [LOWER BOUND(ID), 52 ms]
        (38) typed CpxTrs
        (39) RewriteLemmaProof [LOWER BOUND(ID), 708 ms]
        (40) typed CpxTrs
        (41) RewriteLemmaProof [LOWER BOUND(ID), 705 ms]
        (42) typed CpxTrs
        (43) RewriteLemmaProof [LOWER BOUND(ID), 694 ms]
        (44) BOUNDS(1, INF)


----------------------------------------

(0)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   *(@x, @y) -> #mult(@x, @y)
   +(@x, @y) -> #add(@x, @y)
   appendreverse(@toreverse, @sofar) -> appendreverse#1(@toreverse, @sofar)
   appendreverse#1(::(@a, @as), @sofar) -> appendreverse(@as, ::(@a, @sofar))
   appendreverse#1(nil, @sofar) -> @sofar
   bftMult(@t, @acc) -> bftMult'(tuple#2(::(@t, nil), nil), @acc)
   bftMult'(@queue, @acc) -> bftMult'#1(bftMult'#2(@queue), @acc)
   bftMult'#1(tuple#2(@elem, @queue), @acc) -> bftMult'#3(@elem, @acc, @queue)
   bftMult'#2(tuple#2(@dequeue@1, @dequeue@2)) -> dequeue(@dequeue@1, @dequeue@2)
   bftMult'#3(::(@t, @_@3), @acc, @queue) -> bftMult'#4(@t, @acc, @queue)
   bftMult'#3(nil, @acc, @queue) -> @acc
   bftMult'#4(leaf, @acc, @queue) -> bftMult'(@queue, @acc)
   bftMult'#4(node(@y, @t1, @t2), @acc, @queue) -> bftMult'#5(enqueue(@t2, enqueue(@t1, @queue)), @acc, @y)
   bftMult'#5(@queue', @acc, @y) -> bftMult'(@queue', matrixMult(@acc, @y))
   computeLine(@line, @m, @acc) -> computeLine#1(@line, @acc, @m)
   computeLine#1(::(@x, @xs), @acc, @m) -> computeLine#2(@m, @acc, @x, @xs)
   computeLine#1(nil, @acc, @m) -> @acc
   computeLine#2(::(@l, @ls), @acc, @x, @xs) -> computeLine(@xs, @ls, lineMult(@x, @l, @acc))
   computeLine#2(nil, @acc, @x, @xs) -> nil
   dequeue(@outq, @inq) -> dequeue#1(@outq, @inq)
   dequeue#1(::(@t, @ts), @inq) -> tuple#2(::(@t, nil), tuple#2(@ts, @inq))
   dequeue#1(nil, @inq) -> dequeue#2(reverse(@inq))
   dequeue#2(::(@t, @ts)) -> tuple#2(::(@t, nil), tuple#2(@ts, nil))
   dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
   enqueue(@t, @queue) -> enqueue#1(@queue, @t)
   enqueue#1(tuple#2(@outq, @inq), @t) -> tuple#2(@outq, ::(@t, @inq))
   lineMult(@n, @l1, @l2) -> lineMult#1(@l1, @l2, @n)
   lineMult#1(::(@x, @xs), @l2, @n) -> lineMult#2(@l2, @n, @x, @xs)
   lineMult#1(nil, @l2, @n) -> nil
   lineMult#2(::(@y, @ys), @n, @x, @xs) -> ::(+(*(@x, @n), @y), lineMult(@n, @xs, @ys))
   lineMult#2(nil, @n, @x, @xs) -> ::(*(@x, @n), lineMult(@n, @xs, nil))
   matrixMult(@m1, @m2) -> matrixMult#1(@m1, @m2)
   matrixMult#1(::(@l, @ls), @m2) -> ::(computeLine(@l, @m2, nil), matrixMult(@ls, @m2))
   matrixMult#1(nil, @m2) -> nil
   reverse(@xs) -> appendreverse(@xs, nil)

The (relative) TRS S consists of the following rules:

   #add(#0, @y) -> @y
   #add(#neg(#s(#0)), @y) -> #pred(@y)
   #add(#neg(#s(#s(@x))), @y) -> #pred(#add(#pos(#s(@x)), @y))
   #add(#pos(#s(#0)), @y) -> #succ(@y)
   #add(#pos(#s(#s(@x))), @y) -> #succ(#add(#pos(#s(@x)), @y))
   #mult(#0, #0) -> #0
   #mult(#0, #neg(@y)) -> #0
   #mult(#0, #pos(@y)) -> #0
   #mult(#neg(@x), #0) -> #0
   #mult(#neg(@x), #neg(@y)) -> #pos(#natmult(@x, @y))
   #mult(#neg(@x), #pos(@y)) -> #neg(#natmult(@x, @y))
   #mult(#pos(@x), #0) -> #0
   #mult(#pos(@x), #neg(@y)) -> #neg(#natmult(@x, @y))
   #mult(#pos(@x), #pos(@y)) -> #pos(#natmult(@x, @y))
   #natmult(#0, @y) -> #0
   #natmult(#s(@x), @y) -> #add(#pos(@y), #natmult(@x, @y))
   #pred(#0) -> #neg(#s(#0))
   #pred(#neg(#s(@x))) -> #neg(#s(#s(@x)))
   #pred(#pos(#s(#0))) -> #0
   #pred(#pos(#s(#s(@x)))) -> #pos(#s(@x))
   #succ(#0) -> #pos(#s(#0))
   #succ(#neg(#s(#0))) -> #0
   #succ(#neg(#s(#s(@x)))) -> #neg(#s(@x))
   #succ(#pos(#s(@x))) -> #pos(#s(#s(@x)))

Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

(1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID))
proved innermost termination of relative rules
----------------------------------------

(2)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   *(@x, @y) -> #mult(@x, @y)
   +(@x, @y) -> #add(@x, @y)
   appendreverse(@toreverse, @sofar) -> appendreverse#1(@toreverse, @sofar)
   appendreverse#1(::(@a, @as), @sofar) -> appendreverse(@as, ::(@a, @sofar))
   appendreverse#1(nil, @sofar) -> @sofar
   bftMult(@t, @acc) -> bftMult'(tuple#2(::(@t, nil), nil), @acc)
   bftMult'(@queue, @acc) -> bftMult'#1(bftMult'#2(@queue), @acc)
   bftMult'#1(tuple#2(@elem, @queue), @acc) -> bftMult'#3(@elem, @acc, @queue)
   bftMult'#2(tuple#2(@dequeue@1, @dequeue@2)) -> dequeue(@dequeue@1, @dequeue@2)
   bftMult'#3(::(@t, @_@3), @acc, @queue) -> bftMult'#4(@t, @acc, @queue)
   bftMult'#3(nil, @acc, @queue) -> @acc
   bftMult'#4(leaf, @acc, @queue) -> bftMult'(@queue, @acc)
   bftMult'#4(node(@y, @t1, @t2), @acc, @queue) -> bftMult'#5(enqueue(@t2, enqueue(@t1, @queue)), @acc, @y)
   bftMult'#5(@queue', @acc, @y) -> bftMult'(@queue', matrixMult(@acc, @y))
   computeLine(@line, @m, @acc) -> computeLine#1(@line, @acc, @m)
   computeLine#1(::(@x, @xs), @acc, @m) -> computeLine#2(@m, @acc, @x, @xs)
   computeLine#1(nil, @acc, @m) -> @acc
   computeLine#2(::(@l, @ls), @acc, @x, @xs) -> computeLine(@xs, @ls, lineMult(@x, @l, @acc))
   computeLine#2(nil, @acc, @x, @xs) -> nil
   dequeue(@outq, @inq) -> dequeue#1(@outq, @inq)
   dequeue#1(::(@t, @ts), @inq) -> tuple#2(::(@t, nil), tuple#2(@ts, @inq))
   dequeue#1(nil, @inq) -> dequeue#2(reverse(@inq))
   dequeue#2(::(@t, @ts)) -> tuple#2(::(@t, nil), tuple#2(@ts, nil))
   dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
   enqueue(@t, @queue) -> enqueue#1(@queue, @t)
   enqueue#1(tuple#2(@outq, @inq), @t) -> tuple#2(@outq, ::(@t, @inq))
   lineMult(@n, @l1, @l2) -> lineMult#1(@l1, @l2, @n)
   lineMult#1(::(@x, @xs), @l2, @n) -> lineMult#2(@l2, @n, @x, @xs)
   lineMult#1(nil, @l2, @n) -> nil
   lineMult#2(::(@y, @ys), @n, @x, @xs) -> ::(+(*(@x, @n), @y), lineMult(@n, @xs, @ys))
   lineMult#2(nil, @n, @x, @xs) -> ::(*(@x, @n), lineMult(@n, @xs, nil))
   matrixMult(@m1, @m2) -> matrixMult#1(@m1, @m2)
   matrixMult#1(::(@l, @ls), @m2) -> ::(computeLine(@l, @m2, nil), matrixMult(@ls, @m2))
   matrixMult#1(nil, @m2) -> nil
   reverse(@xs) -> appendreverse(@xs, nil)

The (relative) TRS S consists of the following rules:

   #add(#0, @y) -> @y
   #add(#neg(#s(#0)), @y) -> #pred(@y)
   #add(#neg(#s(#s(@x))), @y) -> #pred(#add(#pos(#s(@x)), @y))
   #add(#pos(#s(#0)), @y) -> #succ(@y)
   #add(#pos(#s(#s(@x))), @y) -> #succ(#add(#pos(#s(@x)), @y))
   #mult(#0, #0) -> #0
   #mult(#0, #neg(@y)) -> #0
   #mult(#0, #pos(@y)) -> #0
   #mult(#neg(@x), #0) -> #0
   #mult(#neg(@x), #neg(@y)) -> #pos(#natmult(@x, @y))
   #mult(#neg(@x), #pos(@y)) -> #neg(#natmult(@x, @y))
   #mult(#pos(@x), #0) -> #0
   #mult(#pos(@x), #neg(@y)) -> #neg(#natmult(@x, @y))
   #mult(#pos(@x), #pos(@y)) -> #pos(#natmult(@x, @y))
   #natmult(#0, @y) -> #0
   #natmult(#s(@x), @y) -> #add(#pos(@y), #natmult(@x, @y))
   #pred(#0) -> #neg(#s(#0))
   #pred(#neg(#s(@x))) -> #neg(#s(#s(@x)))
   #pred(#pos(#s(#0))) -> #0
   #pred(#pos(#s(#s(@x)))) -> #pos(#s(@x))
   #succ(#0) -> #pos(#s(#0))
   #succ(#neg(#s(#0))) -> #0
   #succ(#neg(#s(#s(@x)))) -> #neg(#s(@x))
   #succ(#pos(#s(@x))) -> #pos(#s(#s(@x)))

Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

(3) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))
Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT
----------------------------------------

(4)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   #add(#0, z0) -> z0
   #add(#neg(#s(#0)), z0) -> #pred(z0)
   #add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
   #add(#pos(#s(#0)), z0) -> #succ(z0)
   #add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
   #mult(#0, #0) -> #0
   #mult(#0, #neg(z0)) -> #0
   #mult(#0, #pos(z0)) -> #0
   #mult(#neg(z0), #0) -> #0
   #mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
   #mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
   #mult(#pos(z0), #0) -> #0
   #mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
   #mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
   #natmult(#0, z0) -> #0
   #natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
   #pred(#0) -> #neg(#s(#0))
   #pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
   #pred(#pos(#s(#0))) -> #0
   #pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
   #succ(#0) -> #pos(#s(#0))
   #succ(#neg(#s(#0))) -> #0
   #succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
   #succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
   *(z0, z1) -> #mult(z0, z1)
   +(z0, z1) -> #add(z0, z1)
   appendreverse(z0, z1) -> appendreverse#1(z0, z1)
   appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
   appendreverse#1(nil, z0) -> z0
   bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
   bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
   bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
   bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
   bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
   bftMult'#3(nil, z0, z1) -> z0
   bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
   bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
   bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
   computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
   computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
   computeLine#1(nil, z0, z1) -> z0
   computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
   computeLine#2(nil, z0, z1, z2) -> nil
   dequeue(z0, z1) -> dequeue#1(z0, z1)
   dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
   dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
   dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
   dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
   enqueue(z0, z1) -> enqueue#1(z1, z0)
   enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
   lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
   lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
   lineMult#1(nil, z0, z1) -> nil
   lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+(*(z3, z2), z0), lineMult(z2, z4, z1))
   lineMult#2(nil, z0, z1, z2) -> ::(*(z1, z0), lineMult(z0, z2, nil))
   matrixMult(z0, z1) -> matrixMult#1(z0, z1)
   matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
   matrixMult#1(nil, z0) -> nil
   reverse(z0) -> appendreverse(z0, nil)
Tuples:
   #ADD(#0, z0) -> c
   #ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
   #ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
   #ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
   #ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
   #MULT(#0, #0) -> c5
   #MULT(#0, #neg(z0)) -> c6
   #MULT(#0, #pos(z0)) -> c7
   #MULT(#neg(z0), #0) -> c8
   #MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
   #MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
   #MULT(#pos(z0), #0) -> c11
   #MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
   #MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
   #NATMULT(#0, z0) -> c14
   #NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
   #PRED(#0) -> c16
   #PRED(#neg(#s(z0))) -> c17
   #PRED(#pos(#s(#0))) -> c18
   #PRED(#pos(#s(#s(z0)))) -> c19
   #SUCC(#0) -> c20
   #SUCC(#neg(#s(#0))) -> c21
   #SUCC(#neg(#s(#s(z0)))) -> c22
   #SUCC(#pos(#s(z0))) -> c23
   *'(z0, z1) -> c24(#MULT(z0, z1))
   +'(z0, z1) -> c25(#ADD(z0, z1))
   APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
   APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
   APPENDREVERSE#1(nil, z0) -> c28
   BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
   BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
   BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
   BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
   BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
   BFTMULT'#3(nil, z0, z1) -> c34
   BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
   BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
   BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
   COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
   COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
   COMPUTELINE#1(nil, z0, z1) -> c40
   COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
   COMPUTELINE#2(nil, z0, z1, z2) -> c42
   DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
   DEQUEUE#1(::(z0, z1), z2) -> c44
   DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
   DEQUEUE#2(::(z0, z1)) -> c46
   DEQUEUE#2(nil) -> c47
   ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
   ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
   LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
   LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
   LINEMULT#1(nil, z0, z1) -> c52
   LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*(z3, z2), z0), *'(z3, z2))
   LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
   LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
   LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
   MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
   MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
   MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
   MATRIXMULT#1(nil, z0) -> c60
   REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))
S tuples:
   *'(z0, z1) -> c24(#MULT(z0, z1))
   +'(z0, z1) -> c25(#ADD(z0, z1))
   APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
   APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
   APPENDREVERSE#1(nil, z0) -> c28
   BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
   BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
   BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
   BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
   BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
   BFTMULT'#3(nil, z0, z1) -> c34
   BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
   BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
   BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
   COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
   COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
   COMPUTELINE#1(nil, z0, z1) -> c40
   COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
   COMPUTELINE#2(nil, z0, z1, z2) -> c42
   DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
   DEQUEUE#1(::(z0, z1), z2) -> c44
   DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
   DEQUEUE#2(::(z0, z1)) -> c46
   DEQUEUE#2(nil) -> c47
   ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
   ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
   LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
   LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
   LINEMULT#1(nil, z0, z1) -> c52
   LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*(z3, z2), z0), *'(z3, z2))
   LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
   LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
   LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
   MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
   MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
   MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
   MATRIXMULT#1(nil, z0) -> c60
   REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))
K tuples:none
Defined Rule Symbols:   *_2, +_2, appendreverse_2, appendreverse#1_2, bftMult_2, bftMult'_2, bftMult'#1_2, bftMult'#2_1, bftMult'#3_3, bftMult'#4_3, bftMult'#5_3, computeLine_3, computeLine#1_3, computeLine#2_4, dequeue_2, dequeue#1_2, dequeue#2_1, enqueue_2, enqueue#1_2, lineMult_3, lineMult#1_3, lineMult#2_4, matrixMult_2, matrixMult#1_2, reverse_1, #add_2, #mult_2, #natmult_2, #pred_1, #succ_1

Defined Pair Symbols:   #ADD_2, #MULT_2, #NATMULT_2, #PRED_1, #SUCC_1, *'_2, +'_2, APPENDREVERSE_2, APPENDREVERSE#1_2, BFTMULT_2, BFTMULT'_2, BFTMULT'#1_2, BFTMULT'#2_1, BFTMULT'#3_3, BFTMULT'#4_3, BFTMULT'#5_3, COMPUTELINE_3, COMPUTELINE#1_3, COMPUTELINE#2_4, DEQUEUE_2, DEQUEUE#1_2, DEQUEUE#2_1, ENQUEUE_2, ENQUEUE#1_2, LINEMULT_3, LINEMULT#1_3, LINEMULT#2_4, MATRIXMULT_2, MATRIXMULT#1_2, REVERSE_1

Compound Symbols:   c, c1_1, c2_2, c3_1, c4_2, c5, c6, c7, c8, c9_1, c10_1, c11, c12_1, c13_1, c14, c15_2, c16, c17, c18, c19, c20, c21, c22, c23, c24_1, c25_1, c26_1, c27_1, c28, c29_1, c30_2, c31_1, c32_1, c33_1, c34, c35_1, c36_3, c37_2, c38_1, c39_1, c40, c41_2, c42, c43_1, c44, c45_2, c46, c47, c48_1, c49, c50_1, c51_1, c52, c53_2, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60, c61_1


----------------------------------------

(5) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID))
Converted S to standard rules, and D \ S as well as R to relative rules.
----------------------------------------

(6)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   *'(z0, z1) -> c24(#MULT(z0, z1))
   +'(z0, z1) -> c25(#ADD(z0, z1))
   APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
   APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
   APPENDREVERSE#1(nil, z0) -> c28
   BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
   BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
   BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
   BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
   BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
   BFTMULT'#3(nil, z0, z1) -> c34
   BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
   BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
   BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
   COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
   COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
   COMPUTELINE#1(nil, z0, z1) -> c40
   COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
   COMPUTELINE#2(nil, z0, z1, z2) -> c42
   DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
   DEQUEUE#1(::(z0, z1), z2) -> c44
   DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
   DEQUEUE#2(::(z0, z1)) -> c46
   DEQUEUE#2(nil) -> c47
   ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
   ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
   LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
   LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
   LINEMULT#1(nil, z0, z1) -> c52
   LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*(z3, z2), z0), *'(z3, z2))
   LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
   LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
   LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
   MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
   MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
   MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
   MATRIXMULT#1(nil, z0) -> c60
   REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))

The (relative) TRS S consists of the following rules:

   #ADD(#0, z0) -> c
   #ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
   #ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
   #ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
   #ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
   #MULT(#0, #0) -> c5
   #MULT(#0, #neg(z0)) -> c6
   #MULT(#0, #pos(z0)) -> c7
   #MULT(#neg(z0), #0) -> c8
   #MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
   #MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
   #MULT(#pos(z0), #0) -> c11
   #MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
   #MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
   #NATMULT(#0, z0) -> c14
   #NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
   #PRED(#0) -> c16
   #PRED(#neg(#s(z0))) -> c17
   #PRED(#pos(#s(#0))) -> c18
   #PRED(#pos(#s(#s(z0)))) -> c19
   #SUCC(#0) -> c20
   #SUCC(#neg(#s(#0))) -> c21
   #SUCC(#neg(#s(#s(z0)))) -> c22
   #SUCC(#pos(#s(z0))) -> c23
   #add(#0, z0) -> z0
   #add(#neg(#s(#0)), z0) -> #pred(z0)
   #add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
   #add(#pos(#s(#0)), z0) -> #succ(z0)
   #add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
   #mult(#0, #0) -> #0
   #mult(#0, #neg(z0)) -> #0
   #mult(#0, #pos(z0)) -> #0
   #mult(#neg(z0), #0) -> #0
   #mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
   #mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
   #mult(#pos(z0), #0) -> #0
   #mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
   #mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
   #natmult(#0, z0) -> #0
   #natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
   #pred(#0) -> #neg(#s(#0))
   #pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
   #pred(#pos(#s(#0))) -> #0
   #pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
   #succ(#0) -> #pos(#s(#0))
   #succ(#neg(#s(#0))) -> #0
   #succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
   #succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
   *(z0, z1) -> #mult(z0, z1)
   +(z0, z1) -> #add(z0, z1)
   appendreverse(z0, z1) -> appendreverse#1(z0, z1)
   appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
   appendreverse#1(nil, z0) -> z0
   bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
   bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
   bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
   bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
   bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
   bftMult'#3(nil, z0, z1) -> z0
   bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
   bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
   bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
   computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
   computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
   computeLine#1(nil, z0, z1) -> z0
   computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
   computeLine#2(nil, z0, z1, z2) -> nil
   dequeue(z0, z1) -> dequeue#1(z0, z1)
   dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
   dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
   dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
   dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
   enqueue(z0, z1) -> enqueue#1(z1, z0)
   enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
   lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
   lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
   lineMult#1(nil, z0, z1) -> nil
   lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+(*(z3, z2), z0), lineMult(z2, z4, z1))
   lineMult#2(nil, z0, z1, z2) -> ::(*(z1, z0), lineMult(z0, z2, nil))
   matrixMult(z0, z1) -> matrixMult#1(z0, z1)
   matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
   matrixMult#1(nil, z0) -> nil
   reverse(z0) -> appendreverse(z0, nil)

Rewrite Strategy: INNERMOST
----------------------------------------

(7) RenamingProof (BOTH BOUNDS(ID, ID))
Renamed function symbols to avoid clashes with predefined symbol.
----------------------------------------

(8)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   *'(z0, z1) -> c24(#MULT(z0, z1))
   +'(z0, z1) -> c25(#ADD(z0, z1))
   APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
   APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
   APPENDREVERSE#1(nil, z0) -> c28
   BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
   BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
   BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
   BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
   BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
   BFTMULT'#3(nil, z0, z1) -> c34
   BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
   BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
   BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
   COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
   COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
   COMPUTELINE#1(nil, z0, z1) -> c40
   COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
   COMPUTELINE#2(nil, z0, z1, z2) -> c42
   DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
   DEQUEUE#1(::(z0, z1), z2) -> c44
   DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
   DEQUEUE#2(::(z0, z1)) -> c46
   DEQUEUE#2(nil) -> c47
   ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
   ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
   LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
   LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
   LINEMULT#1(nil, z0, z1) -> c52
   LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*'(z3, z2), z0), *'(z3, z2))
   LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
   LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
   LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
   MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
   MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
   MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
   MATRIXMULT#1(nil, z0) -> c60
   REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))

The (relative) TRS S consists of the following rules:

   #ADD(#0, z0) -> c
   #ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
   #ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
   #ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
   #ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
   #MULT(#0, #0) -> c5
   #MULT(#0, #neg(z0)) -> c6
   #MULT(#0, #pos(z0)) -> c7
   #MULT(#neg(z0), #0) -> c8
   #MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
   #MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
   #MULT(#pos(z0), #0) -> c11
   #MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
   #MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
   #NATMULT(#0, z0) -> c14
   #NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
   #PRED(#0) -> c16
   #PRED(#neg(#s(z0))) -> c17
   #PRED(#pos(#s(#0))) -> c18
   #PRED(#pos(#s(#s(z0)))) -> c19
   #SUCC(#0) -> c20
   #SUCC(#neg(#s(#0))) -> c21
   #SUCC(#neg(#s(#s(z0)))) -> c22
   #SUCC(#pos(#s(z0))) -> c23
   #add(#0, z0) -> z0
   #add(#neg(#s(#0)), z0) -> #pred(z0)
   #add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
   #add(#pos(#s(#0)), z0) -> #succ(z0)
   #add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
   #mult(#0, #0) -> #0
   #mult(#0, #neg(z0)) -> #0
   #mult(#0, #pos(z0)) -> #0
   #mult(#neg(z0), #0) -> #0
   #mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
   #mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
   #mult(#pos(z0), #0) -> #0
   #mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
   #mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
   #natmult(#0, z0) -> #0
   #natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
   #pred(#0) -> #neg(#s(#0))
   #pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
   #pred(#pos(#s(#0))) -> #0
   #pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
   #succ(#0) -> #pos(#s(#0))
   #succ(#neg(#s(#0))) -> #0
   #succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
   #succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
   *'(z0, z1) -> #mult(z0, z1)
   +'(z0, z1) -> #add(z0, z1)
   appendreverse(z0, z1) -> appendreverse#1(z0, z1)
   appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
   appendreverse#1(nil, z0) -> z0
   bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
   bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
   bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
   bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
   bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
   bftMult'#3(nil, z0, z1) -> z0
   bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
   bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
   bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
   computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
   computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
   computeLine#1(nil, z0, z1) -> z0
   computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
   computeLine#2(nil, z0, z1, z2) -> nil
   dequeue(z0, z1) -> dequeue#1(z0, z1)
   dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
   dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
   dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
   dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
   enqueue(z0, z1) -> enqueue#1(z1, z0)
   enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
   lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
   lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
   lineMult#1(nil, z0, z1) -> nil
   lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+'(*'(z3, z2), z0), lineMult(z2, z4, z1))
   lineMult#2(nil, z0, z1, z2) -> ::(*'(z1, z0), lineMult(z0, z2, nil))
   matrixMult(z0, z1) -> matrixMult#1(z0, z1)
   matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
   matrixMult#1(nil, z0) -> nil
   reverse(z0) -> appendreverse(z0, nil)

Rewrite Strategy: INNERMOST
----------------------------------------

(9) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Inferred types.
----------------------------------------

(10)
Obligation:
Innermost TRS:
Rules:
*'(z0, z1) -> c24(#MULT(z0, z1))
+'(z0, z1) -> c25(#ADD(z0, z1))
APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
APPENDREVERSE#1(nil, z0) -> c28
BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
BFTMULT'#3(nil, z0, z1) -> c34
BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
COMPUTELINE#1(nil, z0, z1) -> c40
COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
COMPUTELINE#2(nil, z0, z1, z2) -> c42
DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
DEQUEUE#1(::(z0, z1), z2) -> c44
DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
DEQUEUE#2(::(z0, z1)) -> c46
DEQUEUE#2(nil) -> c47
ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
LINEMULT#1(nil, z0, z1) -> c52
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*'(z3, z2), z0), *'(z3, z2))
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
MATRIXMULT#1(nil, z0) -> c60
REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))
#ADD(#0, z0) -> c
#ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
#ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
#ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#MULT(#0, #0) -> c5
#MULT(#0, #neg(z0)) -> c6
#MULT(#0, #pos(z0)) -> c7
#MULT(#neg(z0), #0) -> c8
#MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
#MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
#MULT(#pos(z0), #0) -> c11
#MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
#MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
#NATMULT(#0, z0) -> c14
#NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
#PRED(#0) -> c16
#PRED(#neg(#s(z0))) -> c17
#PRED(#pos(#s(#0))) -> c18
#PRED(#pos(#s(#s(z0)))) -> c19
#SUCC(#0) -> c20
#SUCC(#neg(#s(#0))) -> c21
#SUCC(#neg(#s(#s(z0)))) -> c22
#SUCC(#pos(#s(z0))) -> c23
#add(#0, z0) -> z0
#add(#neg(#s(#0)), z0) -> #pred(z0)
#add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
#add(#pos(#s(#0)), z0) -> #succ(z0)
#add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
#mult(#0, #0) -> #0
#mult(#0, #neg(z0)) -> #0
#mult(#0, #pos(z0)) -> #0
#mult(#neg(z0), #0) -> #0
#mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
#mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #0) -> #0
#mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
#natmult(#0, z0) -> #0
#natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
#pred(#0) -> #neg(#s(#0))
#pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
#pred(#pos(#s(#0))) -> #0
#pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
#succ(#0) -> #pos(#s(#0))
#succ(#neg(#s(#0))) -> #0
#succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
#succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
*'(z0, z1) -> #mult(z0, z1)
+'(z0, z1) -> #add(z0, z1)
appendreverse(z0, z1) -> appendreverse#1(z0, z1)
appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
appendreverse#1(nil, z0) -> z0
bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
bftMult'#3(nil, z0, z1) -> z0
bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
computeLine#1(nil, z0, z1) -> z0
computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
computeLine#2(nil, z0, z1, z2) -> nil
dequeue(z0, z1) -> dequeue#1(z0, z1)
dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
enqueue(z0, z1) -> enqueue#1(z1, z0)
enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
lineMult#1(nil, z0, z1) -> nil
lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+'(*'(z3, z2), z0), lineMult(z2, z4, z1))
lineMult#2(nil, z0, z1, z2) -> ::(*'(z1, z0), lineMult(z0, z2, nil))
matrixMult(z0, z1) -> matrixMult#1(z0, z1)
matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
matrixMult#1(nil, z0) -> nil
reverse(z0) -> appendreverse(z0, nil)

Types:
*' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c24 :: c5:c6:c7:c8:c9:c10:c11:c12:c13 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#MULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c5:c6:c7:c8:c9:c10:c11:c12:c13
+' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c25 :: c:c1:c2:c3:c4 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#ADD :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c:c1:c2:c3:c4
APPENDREVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c26
c26 :: c27:c28 -> c26
APPENDREVERSE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c27:c28
:: :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c27 :: c26 -> c27:c28
nil :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c28 :: c27:c28
BFTMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c29
c29 :: c30 -> c29
BFTMULT' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c30
tuple#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c30 :: c31 -> c32 -> c30
BFTMULT'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c31
bftMult'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
BFTMULT'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c32
c31 :: c33:c34 -> c31
BFTMULT'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c33:c34
c32 :: c43 -> c32
DEQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c43
c33 :: c35:c36 -> c33:c34
BFTMULT'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c35:c36
c34 :: c33:c34
leaf :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c35 :: c30 -> c35:c36
node :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c36 :: c37 -> c48 -> c48 -> c35:c36
BFTMULT'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c37
enqueue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
ENQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c48
c37 :: c30 -> c57 -> c37
matrixMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
MATRIXMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c57
COMPUTELINE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c38
c38 :: c39:c40 -> c38
COMPUTELINE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c39:c40
c39 :: c41:c42 -> c39:c40
COMPUTELINE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c41:c42
c40 :: c39:c40
c41 :: c38 -> c50 -> c41:c42
lineMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
LINEMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c50
c42 :: c41:c42
c43 :: c44:c45 -> c43
DEQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c44:c45
c44 :: c44:c45
c45 :: c46:c47 -> c61 -> c44:c45
DEQUEUE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c46:c47
reverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
REVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c61
c46 :: c46:c47
c47 :: c46:c47
c48 :: c49 -> c48
ENQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c49
c49 :: c49
c50 :: c51:c52 -> c50
LINEMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c51:c52
c51 :: c53:c54:c55:c56 -> c51:c52
LINEMULT#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c52 :: c51:c52
c53 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c54 :: c50 -> c53:c54:c55:c56
c55 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c56 :: c50 -> c53:c54:c55:c56
c57 :: c58:c59:c60 -> c57
MATRIXMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c58:c59:c60
c58 :: c38 -> c58:c59:c60
c59 :: c57 -> c58:c59:c60
c60 :: c58:c59:c60
c61 :: c26 -> c61
#0 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c :: c:c1:c2:c3:c4
#neg :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#s :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c1 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4
#PRED :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c16:c17:c18:c19
c2 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
#add :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#pos :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c3 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4
#SUCC :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c20:c21:c22:c23
c4 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
c5 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c6 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c7 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c8 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c9 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
#NATMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c14:c15
c10 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c11 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c12 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c13 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c14 :: c14:c15
c15 :: c:c1:c2:c3:c4 -> c14:c15 -> c14:c15
#natmult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c16 :: c16:c17:c18:c19
c17 :: c16:c17:c18:c19
c18 :: c16:c17:c18:c19
c19 :: c16:c17:c18:c19
c20 :: c20:c21:c22:c23
c21 :: c20:c21:c22:c23
c22 :: c20:c21:c22:c23
c23 :: c20:c21:c22:c23
#pred :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#succ :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#mult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
enqueue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
matrixMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos1_62 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c5:c6:c7:c8:c9:c10:c11:c12:c132_62 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
hole_c:c1:c2:c3:c43_62 :: c:c1:c2:c3:c4
hole_c264_62 :: c26
hole_c27:c285_62 :: c27:c28
hole_c296_62 :: c29
hole_c307_62 :: c30
hole_c318_62 :: c31
hole_c329_62 :: c32
hole_c33:c3410_62 :: c33:c34
hole_c4311_62 :: c43
hole_c35:c3612_62 :: c35:c36
hole_c3713_62 :: c37
hole_c4814_62 :: c48
hole_c5715_62 :: c57
hole_c3816_62 :: c38
hole_c39:c4017_62 :: c39:c40
hole_c41:c4218_62 :: c41:c42
hole_c5019_62 :: c50
hole_c44:c4520_62 :: c44:c45
hole_c46:c4721_62 :: c46:c47
hole_c6122_62 :: c61
hole_c4923_62 :: c49
hole_c51:c5224_62 :: c51:c52
hole_c53:c54:c55:c5625_62 :: c53:c54:c55:c56
hole_c58:c59:c6026_62 :: c58:c59:c60
hole_c16:c17:c18:c1927_62 :: c16:c17:c18:c19
hole_c20:c21:c22:c2328_62 :: c20:c21:c22:c23
hole_c14:c1529_62 :: c14:c15
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62 :: Nat -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
gen_c:c1:c2:c3:c431_62 :: Nat -> c:c1:c2:c3:c4
gen_c14:c1532_62 :: Nat -> c14:c15

----------------------------------------

(11) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
#ADD, APPENDREVERSE, APPENDREVERSE#1, BFTMULT', BFTMULT'#1, matrixMult, MATRIXMULT, COMPUTELINE, COMPUTELINE#1, lineMult, LINEMULT, LINEMULT#1, MATRIXMULT#1, #add, #NATMULT, #natmult, appendreverse, appendreverse#1, bftMult', bftMult'#1, computeLine, computeLine#1, lineMult#1, matrixMult#1

They will be analysed ascendingly in the following order:
#add < #ADD
#ADD < #NATMULT
APPENDREVERSE = APPENDREVERSE#1
BFTMULT' = BFTMULT'#1
matrixMult < BFTMULT'#1
MATRIXMULT < BFTMULT'#1
matrixMult < bftMult'#1
matrixMult = matrixMult#1
MATRIXMULT = MATRIXMULT#1
COMPUTELINE = COMPUTELINE#1
COMPUTELINE < MATRIXMULT#1
lineMult < COMPUTELINE#1
LINEMULT < COMPUTELINE#1
lineMult < computeLine#1
lineMult = lineMult#1
LINEMULT = LINEMULT#1
#add < #natmult
#natmult < #NATMULT
appendreverse = appendreverse#1
bftMult' = bftMult'#1
computeLine = computeLine#1
computeLine < matrixMult#1

----------------------------------------

(12)
Obligation:
Innermost TRS:
Rules:
*'(z0, z1) -> c24(#MULT(z0, z1))
+'(z0, z1) -> c25(#ADD(z0, z1))
APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
APPENDREVERSE#1(nil, z0) -> c28
BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
BFTMULT'#3(nil, z0, z1) -> c34
BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
COMPUTELINE#1(nil, z0, z1) -> c40
COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
COMPUTELINE#2(nil, z0, z1, z2) -> c42
DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
DEQUEUE#1(::(z0, z1), z2) -> c44
DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
DEQUEUE#2(::(z0, z1)) -> c46
DEQUEUE#2(nil) -> c47
ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
LINEMULT#1(nil, z0, z1) -> c52
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*'(z3, z2), z0), *'(z3, z2))
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
MATRIXMULT#1(nil, z0) -> c60
REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))
#ADD(#0, z0) -> c
#ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
#ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
#ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#MULT(#0, #0) -> c5
#MULT(#0, #neg(z0)) -> c6
#MULT(#0, #pos(z0)) -> c7
#MULT(#neg(z0), #0) -> c8
#MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
#MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
#MULT(#pos(z0), #0) -> c11
#MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
#MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
#NATMULT(#0, z0) -> c14
#NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
#PRED(#0) -> c16
#PRED(#neg(#s(z0))) -> c17
#PRED(#pos(#s(#0))) -> c18
#PRED(#pos(#s(#s(z0)))) -> c19
#SUCC(#0) -> c20
#SUCC(#neg(#s(#0))) -> c21
#SUCC(#neg(#s(#s(z0)))) -> c22
#SUCC(#pos(#s(z0))) -> c23
#add(#0, z0) -> z0
#add(#neg(#s(#0)), z0) -> #pred(z0)
#add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
#add(#pos(#s(#0)), z0) -> #succ(z0)
#add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
#mult(#0, #0) -> #0
#mult(#0, #neg(z0)) -> #0
#mult(#0, #pos(z0)) -> #0
#mult(#neg(z0), #0) -> #0
#mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
#mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #0) -> #0
#mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
#natmult(#0, z0) -> #0
#natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
#pred(#0) -> #neg(#s(#0))
#pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
#pred(#pos(#s(#0))) -> #0
#pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
#succ(#0) -> #pos(#s(#0))
#succ(#neg(#s(#0))) -> #0
#succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
#succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
*'(z0, z1) -> #mult(z0, z1)
+'(z0, z1) -> #add(z0, z1)
appendreverse(z0, z1) -> appendreverse#1(z0, z1)
appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
appendreverse#1(nil, z0) -> z0
bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
bftMult'#3(nil, z0, z1) -> z0
bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
computeLine#1(nil, z0, z1) -> z0
computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
computeLine#2(nil, z0, z1, z2) -> nil
dequeue(z0, z1) -> dequeue#1(z0, z1)
dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
enqueue(z0, z1) -> enqueue#1(z1, z0)
enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
lineMult#1(nil, z0, z1) -> nil
lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+'(*'(z3, z2), z0), lineMult(z2, z4, z1))
lineMult#2(nil, z0, z1, z2) -> ::(*'(z1, z0), lineMult(z0, z2, nil))
matrixMult(z0, z1) -> matrixMult#1(z0, z1)
matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
matrixMult#1(nil, z0) -> nil
reverse(z0) -> appendreverse(z0, nil)

Types:
*' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c24 :: c5:c6:c7:c8:c9:c10:c11:c12:c13 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#MULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c5:c6:c7:c8:c9:c10:c11:c12:c13
+' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c25 :: c:c1:c2:c3:c4 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#ADD :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c:c1:c2:c3:c4
APPENDREVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c26
c26 :: c27:c28 -> c26
APPENDREVERSE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c27:c28
:: :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c27 :: c26 -> c27:c28
nil :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c28 :: c27:c28
BFTMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c29
c29 :: c30 -> c29
BFTMULT' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c30
tuple#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c30 :: c31 -> c32 -> c30
BFTMULT'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c31
bftMult'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
BFTMULT'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c32
c31 :: c33:c34 -> c31
BFTMULT'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c33:c34
c32 :: c43 -> c32
DEQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c43
c33 :: c35:c36 -> c33:c34
BFTMULT'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c35:c36
c34 :: c33:c34
leaf :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c35 :: c30 -> c35:c36
node :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c36 :: c37 -> c48 -> c48 -> c35:c36
BFTMULT'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c37
enqueue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
ENQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c48
c37 :: c30 -> c57 -> c37
matrixMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
MATRIXMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c57
COMPUTELINE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c38
c38 :: c39:c40 -> c38
COMPUTELINE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c39:c40
c39 :: c41:c42 -> c39:c40
COMPUTELINE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c41:c42
c40 :: c39:c40
c41 :: c38 -> c50 -> c41:c42
lineMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
LINEMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c50
c42 :: c41:c42
c43 :: c44:c45 -> c43
DEQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c44:c45
c44 :: c44:c45
c45 :: c46:c47 -> c61 -> c44:c45
DEQUEUE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c46:c47
reverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
REVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c61
c46 :: c46:c47
c47 :: c46:c47
c48 :: c49 -> c48
ENQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c49
c49 :: c49
c50 :: c51:c52 -> c50
LINEMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c51:c52
c51 :: c53:c54:c55:c56 -> c51:c52
LINEMULT#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c52 :: c51:c52
c53 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c54 :: c50 -> c53:c54:c55:c56
c55 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c56 :: c50 -> c53:c54:c55:c56
c57 :: c58:c59:c60 -> c57
MATRIXMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c58:c59:c60
c58 :: c38 -> c58:c59:c60
c59 :: c57 -> c58:c59:c60
c60 :: c58:c59:c60
c61 :: c26 -> c61
#0 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c :: c:c1:c2:c3:c4
#neg :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#s :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c1 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4
#PRED :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c16:c17:c18:c19
c2 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
#add :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#pos :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c3 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4
#SUCC :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c20:c21:c22:c23
c4 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
c5 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c6 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c7 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c8 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c9 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
#NATMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c14:c15
c10 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c11 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c12 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c13 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c14 :: c14:c15
c15 :: c:c1:c2:c3:c4 -> c14:c15 -> c14:c15
#natmult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c16 :: c16:c17:c18:c19
c17 :: c16:c17:c18:c19
c18 :: c16:c17:c18:c19
c19 :: c16:c17:c18:c19
c20 :: c20:c21:c22:c23
c21 :: c20:c21:c22:c23
c22 :: c20:c21:c22:c23
c23 :: c20:c21:c22:c23
#pred :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#succ :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#mult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
enqueue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
matrixMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos1_62 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c5:c6:c7:c8:c9:c10:c11:c12:c132_62 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
hole_c:c1:c2:c3:c43_62 :: c:c1:c2:c3:c4
hole_c264_62 :: c26
hole_c27:c285_62 :: c27:c28
hole_c296_62 :: c29
hole_c307_62 :: c30
hole_c318_62 :: c31
hole_c329_62 :: c32
hole_c33:c3410_62 :: c33:c34
hole_c4311_62 :: c43
hole_c35:c3612_62 :: c35:c36
hole_c3713_62 :: c37
hole_c4814_62 :: c48
hole_c5715_62 :: c57
hole_c3816_62 :: c38
hole_c39:c4017_62 :: c39:c40
hole_c41:c4218_62 :: c41:c42
hole_c5019_62 :: c50
hole_c44:c4520_62 :: c44:c45
hole_c46:c4721_62 :: c46:c47
hole_c6122_62 :: c61
hole_c4923_62 :: c49
hole_c51:c5224_62 :: c51:c52
hole_c53:c54:c55:c5625_62 :: c53:c54:c55:c56
hole_c58:c59:c6026_62 :: c58:c59:c60
hole_c16:c17:c18:c1927_62 :: c16:c17:c18:c19
hole_c20:c21:c22:c2328_62 :: c20:c21:c22:c23
hole_c14:c1529_62 :: c14:c15
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62 :: Nat -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
gen_c:c1:c2:c3:c431_62 :: Nat -> c:c1:c2:c3:c4
gen_c14:c1532_62 :: Nat -> c14:c15


Generator Equations:
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0) <=> nil
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(x, 1)) <=> ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(x))
gen_c:c1:c2:c3:c431_62(0) <=> c
gen_c:c1:c2:c3:c431_62(+(x, 1)) <=> c2(c16, gen_c:c1:c2:c3:c431_62(x))
gen_c14:c1532_62(0) <=> c14
gen_c14:c1532_62(+(x, 1)) <=> c15(c, gen_c14:c1532_62(x))


The following defined symbols remain to be analysed:
#add, #ADD, APPENDREVERSE, APPENDREVERSE#1, BFTMULT', BFTMULT'#1, matrixMult, MATRIXMULT, COMPUTELINE, COMPUTELINE#1, lineMult, LINEMULT, LINEMULT#1, MATRIXMULT#1, #NATMULT, #natmult, appendreverse, appendreverse#1, bftMult', bftMult'#1, computeLine, computeLine#1, lineMult#1, matrixMult#1

They will be analysed ascendingly in the following order:
#add < #ADD
#ADD < #NATMULT
APPENDREVERSE = APPENDREVERSE#1
BFTMULT' = BFTMULT'#1
matrixMult < BFTMULT'#1
MATRIXMULT < BFTMULT'#1
matrixMult < bftMult'#1
matrixMult = matrixMult#1
MATRIXMULT = MATRIXMULT#1
COMPUTELINE = COMPUTELINE#1
COMPUTELINE < MATRIXMULT#1
lineMult < COMPUTELINE#1
LINEMULT < COMPUTELINE#1
lineMult < computeLine#1
lineMult = lineMult#1
LINEMULT = LINEMULT#1
#add < #natmult
#natmult < #NATMULT
appendreverse = appendreverse#1
bftMult' = bftMult'#1
computeLine = computeLine#1
computeLine < matrixMult#1

----------------------------------------

(13) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
appendreverse#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n250_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n250_62, b)), rt in Omega(0)

Induction Base:
appendreverse#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) ->_R^Omega(0)
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)

Induction Step:
appendreverse#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n250_62, 1)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) ->_R^Omega(0)
appendreverse(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n250_62), ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))) ->_R^Omega(0)
appendreverse#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n250_62), ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))) ->_IH
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(+(b, 1), c251_62))

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(14)
Obligation:
Innermost TRS:
Rules:
*'(z0, z1) -> c24(#MULT(z0, z1))
+'(z0, z1) -> c25(#ADD(z0, z1))
APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
APPENDREVERSE#1(nil, z0) -> c28
BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
BFTMULT'#3(nil, z0, z1) -> c34
BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
COMPUTELINE#1(nil, z0, z1) -> c40
COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
COMPUTELINE#2(nil, z0, z1, z2) -> c42
DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
DEQUEUE#1(::(z0, z1), z2) -> c44
DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
DEQUEUE#2(::(z0, z1)) -> c46
DEQUEUE#2(nil) -> c47
ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
LINEMULT#1(nil, z0, z1) -> c52
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*'(z3, z2), z0), *'(z3, z2))
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
MATRIXMULT#1(nil, z0) -> c60
REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))
#ADD(#0, z0) -> c
#ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
#ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
#ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#MULT(#0, #0) -> c5
#MULT(#0, #neg(z0)) -> c6
#MULT(#0, #pos(z0)) -> c7
#MULT(#neg(z0), #0) -> c8
#MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
#MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
#MULT(#pos(z0), #0) -> c11
#MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
#MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
#NATMULT(#0, z0) -> c14
#NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
#PRED(#0) -> c16
#PRED(#neg(#s(z0))) -> c17
#PRED(#pos(#s(#0))) -> c18
#PRED(#pos(#s(#s(z0)))) -> c19
#SUCC(#0) -> c20
#SUCC(#neg(#s(#0))) -> c21
#SUCC(#neg(#s(#s(z0)))) -> c22
#SUCC(#pos(#s(z0))) -> c23
#add(#0, z0) -> z0
#add(#neg(#s(#0)), z0) -> #pred(z0)
#add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
#add(#pos(#s(#0)), z0) -> #succ(z0)
#add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
#mult(#0, #0) -> #0
#mult(#0, #neg(z0)) -> #0
#mult(#0, #pos(z0)) -> #0
#mult(#neg(z0), #0) -> #0
#mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
#mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #0) -> #0
#mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
#natmult(#0, z0) -> #0
#natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
#pred(#0) -> #neg(#s(#0))
#pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
#pred(#pos(#s(#0))) -> #0
#pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
#succ(#0) -> #pos(#s(#0))
#succ(#neg(#s(#0))) -> #0
#succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
#succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
*'(z0, z1) -> #mult(z0, z1)
+'(z0, z1) -> #add(z0, z1)
appendreverse(z0, z1) -> appendreverse#1(z0, z1)
appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
appendreverse#1(nil, z0) -> z0
bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
bftMult'#3(nil, z0, z1) -> z0
bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
computeLine#1(nil, z0, z1) -> z0
computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
computeLine#2(nil, z0, z1, z2) -> nil
dequeue(z0, z1) -> dequeue#1(z0, z1)
dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
enqueue(z0, z1) -> enqueue#1(z1, z0)
enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
lineMult#1(nil, z0, z1) -> nil
lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+'(*'(z3, z2), z0), lineMult(z2, z4, z1))
lineMult#2(nil, z0, z1, z2) -> ::(*'(z1, z0), lineMult(z0, z2, nil))
matrixMult(z0, z1) -> matrixMult#1(z0, z1)
matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
matrixMult#1(nil, z0) -> nil
reverse(z0) -> appendreverse(z0, nil)

Types:
*' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c24 :: c5:c6:c7:c8:c9:c10:c11:c12:c13 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#MULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c5:c6:c7:c8:c9:c10:c11:c12:c13
+' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c25 :: c:c1:c2:c3:c4 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#ADD :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c:c1:c2:c3:c4
APPENDREVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c26
c26 :: c27:c28 -> c26
APPENDREVERSE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c27:c28
:: :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c27 :: c26 -> c27:c28
nil :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c28 :: c27:c28
BFTMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c29
c29 :: c30 -> c29
BFTMULT' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c30
tuple#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c30 :: c31 -> c32 -> c30
BFTMULT'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c31
bftMult'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
BFTMULT'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c32
c31 :: c33:c34 -> c31
BFTMULT'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c33:c34
c32 :: c43 -> c32
DEQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c43
c33 :: c35:c36 -> c33:c34
BFTMULT'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c35:c36
c34 :: c33:c34
leaf :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c35 :: c30 -> c35:c36
node :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c36 :: c37 -> c48 -> c48 -> c35:c36
BFTMULT'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c37
enqueue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
ENQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c48
c37 :: c30 -> c57 -> c37
matrixMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
MATRIXMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c57
COMPUTELINE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c38
c38 :: c39:c40 -> c38
COMPUTELINE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c39:c40
c39 :: c41:c42 -> c39:c40
COMPUTELINE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c41:c42
c40 :: c39:c40
c41 :: c38 -> c50 -> c41:c42
lineMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
LINEMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c50
c42 :: c41:c42
c43 :: c44:c45 -> c43
DEQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c44:c45
c44 :: c44:c45
c45 :: c46:c47 -> c61 -> c44:c45
DEQUEUE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c46:c47
reverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
REVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c61
c46 :: c46:c47
c47 :: c46:c47
c48 :: c49 -> c48
ENQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c49
c49 :: c49
c50 :: c51:c52 -> c50
LINEMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c51:c52
c51 :: c53:c54:c55:c56 -> c51:c52
LINEMULT#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c52 :: c51:c52
c53 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c54 :: c50 -> c53:c54:c55:c56
c55 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c56 :: c50 -> c53:c54:c55:c56
c57 :: c58:c59:c60 -> c57
MATRIXMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c58:c59:c60
c58 :: c38 -> c58:c59:c60
c59 :: c57 -> c58:c59:c60
c60 :: c58:c59:c60
c61 :: c26 -> c61
#0 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c :: c:c1:c2:c3:c4
#neg :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#s :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c1 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4
#PRED :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c16:c17:c18:c19
c2 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
#add :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#pos :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c3 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4
#SUCC :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c20:c21:c22:c23
c4 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
c5 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c6 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c7 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c8 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c9 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
#NATMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c14:c15
c10 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c11 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c12 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c13 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c14 :: c14:c15
c15 :: c:c1:c2:c3:c4 -> c14:c15 -> c14:c15
#natmult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c16 :: c16:c17:c18:c19
c17 :: c16:c17:c18:c19
c18 :: c16:c17:c18:c19
c19 :: c16:c17:c18:c19
c20 :: c20:c21:c22:c23
c21 :: c20:c21:c22:c23
c22 :: c20:c21:c22:c23
c23 :: c20:c21:c22:c23
#pred :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#succ :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#mult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
enqueue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
matrixMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos1_62 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c5:c6:c7:c8:c9:c10:c11:c12:c132_62 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
hole_c:c1:c2:c3:c43_62 :: c:c1:c2:c3:c4
hole_c264_62 :: c26
hole_c27:c285_62 :: c27:c28
hole_c296_62 :: c29
hole_c307_62 :: c30
hole_c318_62 :: c31
hole_c329_62 :: c32
hole_c33:c3410_62 :: c33:c34
hole_c4311_62 :: c43
hole_c35:c3612_62 :: c35:c36
hole_c3713_62 :: c37
hole_c4814_62 :: c48
hole_c5715_62 :: c57
hole_c3816_62 :: c38
hole_c39:c4017_62 :: c39:c40
hole_c41:c4218_62 :: c41:c42
hole_c5019_62 :: c50
hole_c44:c4520_62 :: c44:c45
hole_c46:c4721_62 :: c46:c47
hole_c6122_62 :: c61
hole_c4923_62 :: c49
hole_c51:c5224_62 :: c51:c52
hole_c53:c54:c55:c5625_62 :: c53:c54:c55:c56
hole_c58:c59:c6026_62 :: c58:c59:c60
hole_c16:c17:c18:c1927_62 :: c16:c17:c18:c19
hole_c20:c21:c22:c2328_62 :: c20:c21:c22:c23
hole_c14:c1529_62 :: c14:c15
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62 :: Nat -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
gen_c:c1:c2:c3:c431_62 :: Nat -> c:c1:c2:c3:c4
gen_c14:c1532_62 :: Nat -> c14:c15


Lemmas:
appendreverse#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n250_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n250_62, b)), rt in Omega(0)


Generator Equations:
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0) <=> nil
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(x, 1)) <=> ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(x))
gen_c:c1:c2:c3:c431_62(0) <=> c
gen_c:c1:c2:c3:c431_62(+(x, 1)) <=> c2(c16, gen_c:c1:c2:c3:c431_62(x))
gen_c14:c1532_62(0) <=> c14
gen_c14:c1532_62(+(x, 1)) <=> c15(c, gen_c14:c1532_62(x))


The following defined symbols remain to be analysed:
appendreverse, APPENDREVERSE, APPENDREVERSE#1, BFTMULT', BFTMULT'#1, matrixMult, MATRIXMULT, COMPUTELINE, COMPUTELINE#1, lineMult, LINEMULT, LINEMULT#1, MATRIXMULT#1, bftMult', bftMult'#1, computeLine, computeLine#1, lineMult#1, matrixMult#1

They will be analysed ascendingly in the following order:
APPENDREVERSE = APPENDREVERSE#1
BFTMULT' = BFTMULT'#1
matrixMult < BFTMULT'#1
MATRIXMULT < BFTMULT'#1
matrixMult < bftMult'#1
matrixMult = matrixMult#1
MATRIXMULT = MATRIXMULT#1
COMPUTELINE = COMPUTELINE#1
COMPUTELINE < MATRIXMULT#1
lineMult < COMPUTELINE#1
LINEMULT < COMPUTELINE#1
lineMult < computeLine#1
lineMult = lineMult#1
LINEMULT = LINEMULT#1
appendreverse = appendreverse#1
bftMult' = bftMult'#1
computeLine = computeLine#1
computeLine < matrixMult#1

----------------------------------------

(15) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n4238_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n4238_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n4238_62)

Induction Base:
LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, 0)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c))

Induction Step:
LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, +(n4238_62, 1))), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n4238_62, 1)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) ->_R^Omega(1)
c51(LINEMULT#2(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n4238_62, 1)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c), nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n4238_62)))) ->_R^Omega(1)
c51(c54(LINEMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n4238_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n4238_62)))) ->_R^Omega(1)
c51(c54(c50(LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n4238_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n4238_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c))))) ->_IH
c51(c54(c50(*33_62)))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(16)
Complex Obligation (BEST)

----------------------------------------

(17)
Obligation:
Proved the lower bound n^1 for the following obligation:

Innermost TRS:
Rules:
*'(z0, z1) -> c24(#MULT(z0, z1))
+'(z0, z1) -> c25(#ADD(z0, z1))
APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
APPENDREVERSE#1(nil, z0) -> c28
BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
BFTMULT'#3(nil, z0, z1) -> c34
BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
COMPUTELINE#1(nil, z0, z1) -> c40
COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
COMPUTELINE#2(nil, z0, z1, z2) -> c42
DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
DEQUEUE#1(::(z0, z1), z2) -> c44
DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
DEQUEUE#2(::(z0, z1)) -> c46
DEQUEUE#2(nil) -> c47
ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
LINEMULT#1(nil, z0, z1) -> c52
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*'(z3, z2), z0), *'(z3, z2))
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
MATRIXMULT#1(nil, z0) -> c60
REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))
#ADD(#0, z0) -> c
#ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
#ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
#ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#MULT(#0, #0) -> c5
#MULT(#0, #neg(z0)) -> c6
#MULT(#0, #pos(z0)) -> c7
#MULT(#neg(z0), #0) -> c8
#MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
#MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
#MULT(#pos(z0), #0) -> c11
#MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
#MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
#NATMULT(#0, z0) -> c14
#NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
#PRED(#0) -> c16
#PRED(#neg(#s(z0))) -> c17
#PRED(#pos(#s(#0))) -> c18
#PRED(#pos(#s(#s(z0)))) -> c19
#SUCC(#0) -> c20
#SUCC(#neg(#s(#0))) -> c21
#SUCC(#neg(#s(#s(z0)))) -> c22
#SUCC(#pos(#s(z0))) -> c23
#add(#0, z0) -> z0
#add(#neg(#s(#0)), z0) -> #pred(z0)
#add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
#add(#pos(#s(#0)), z0) -> #succ(z0)
#add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
#mult(#0, #0) -> #0
#mult(#0, #neg(z0)) -> #0
#mult(#0, #pos(z0)) -> #0
#mult(#neg(z0), #0) -> #0
#mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
#mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #0) -> #0
#mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
#natmult(#0, z0) -> #0
#natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
#pred(#0) -> #neg(#s(#0))
#pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
#pred(#pos(#s(#0))) -> #0
#pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
#succ(#0) -> #pos(#s(#0))
#succ(#neg(#s(#0))) -> #0
#succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
#succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
*'(z0, z1) -> #mult(z0, z1)
+'(z0, z1) -> #add(z0, z1)
appendreverse(z0, z1) -> appendreverse#1(z0, z1)
appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
appendreverse#1(nil, z0) -> z0
bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
bftMult'#3(nil, z0, z1) -> z0
bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
computeLine#1(nil, z0, z1) -> z0
computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
computeLine#2(nil, z0, z1, z2) -> nil
dequeue(z0, z1) -> dequeue#1(z0, z1)
dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
enqueue(z0, z1) -> enqueue#1(z1, z0)
enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
lineMult#1(nil, z0, z1) -> nil
lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+'(*'(z3, z2), z0), lineMult(z2, z4, z1))
lineMult#2(nil, z0, z1, z2) -> ::(*'(z1, z0), lineMult(z0, z2, nil))
matrixMult(z0, z1) -> matrixMult#1(z0, z1)
matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
matrixMult#1(nil, z0) -> nil
reverse(z0) -> appendreverse(z0, nil)

Types:
*' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c24 :: c5:c6:c7:c8:c9:c10:c11:c12:c13 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#MULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c5:c6:c7:c8:c9:c10:c11:c12:c13
+' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c25 :: c:c1:c2:c3:c4 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#ADD :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c:c1:c2:c3:c4
APPENDREVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c26
c26 :: c27:c28 -> c26
APPENDREVERSE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c27:c28
:: :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c27 :: c26 -> c27:c28
nil :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c28 :: c27:c28
BFTMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c29
c29 :: c30 -> c29
BFTMULT' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c30
tuple#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c30 :: c31 -> c32 -> c30
BFTMULT'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c31
bftMult'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
BFTMULT'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c32
c31 :: c33:c34 -> c31
BFTMULT'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c33:c34
c32 :: c43 -> c32
DEQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c43
c33 :: c35:c36 -> c33:c34
BFTMULT'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c35:c36
c34 :: c33:c34
leaf :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c35 :: c30 -> c35:c36
node :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c36 :: c37 -> c48 -> c48 -> c35:c36
BFTMULT'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c37
enqueue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
ENQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c48
c37 :: c30 -> c57 -> c37
matrixMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
MATRIXMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c57
COMPUTELINE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c38
c38 :: c39:c40 -> c38
COMPUTELINE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c39:c40
c39 :: c41:c42 -> c39:c40
COMPUTELINE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c41:c42
c40 :: c39:c40
c41 :: c38 -> c50 -> c41:c42
lineMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
LINEMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c50
c42 :: c41:c42
c43 :: c44:c45 -> c43
DEQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c44:c45
c44 :: c44:c45
c45 :: c46:c47 -> c61 -> c44:c45
DEQUEUE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c46:c47
reverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
REVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c61
c46 :: c46:c47
c47 :: c46:c47
c48 :: c49 -> c48
ENQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c49
c49 :: c49
c50 :: c51:c52 -> c50
LINEMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c51:c52
c51 :: c53:c54:c55:c56 -> c51:c52
LINEMULT#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c52 :: c51:c52
c53 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c54 :: c50 -> c53:c54:c55:c56
c55 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c56 :: c50 -> c53:c54:c55:c56
c57 :: c58:c59:c60 -> c57
MATRIXMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c58:c59:c60
c58 :: c38 -> c58:c59:c60
c59 :: c57 -> c58:c59:c60
c60 :: c58:c59:c60
c61 :: c26 -> c61
#0 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c :: c:c1:c2:c3:c4
#neg :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#s :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c1 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4
#PRED :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c16:c17:c18:c19
c2 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
#add :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#pos :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c3 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4
#SUCC :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c20:c21:c22:c23
c4 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
c5 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c6 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c7 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c8 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c9 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
#NATMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c14:c15
c10 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c11 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c12 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c13 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c14 :: c14:c15
c15 :: c:c1:c2:c3:c4 -> c14:c15 -> c14:c15
#natmult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c16 :: c16:c17:c18:c19
c17 :: c16:c17:c18:c19
c18 :: c16:c17:c18:c19
c19 :: c16:c17:c18:c19
c20 :: c20:c21:c22:c23
c21 :: c20:c21:c22:c23
c22 :: c20:c21:c22:c23
c23 :: c20:c21:c22:c23
#pred :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#succ :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#mult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
enqueue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
matrixMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos1_62 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c5:c6:c7:c8:c9:c10:c11:c12:c132_62 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
hole_c:c1:c2:c3:c43_62 :: c:c1:c2:c3:c4
hole_c264_62 :: c26
hole_c27:c285_62 :: c27:c28
hole_c296_62 :: c29
hole_c307_62 :: c30
hole_c318_62 :: c31
hole_c329_62 :: c32
hole_c33:c3410_62 :: c33:c34
hole_c4311_62 :: c43
hole_c35:c3612_62 :: c35:c36
hole_c3713_62 :: c37
hole_c4814_62 :: c48
hole_c5715_62 :: c57
hole_c3816_62 :: c38
hole_c39:c4017_62 :: c39:c40
hole_c41:c4218_62 :: c41:c42
hole_c5019_62 :: c50
hole_c44:c4520_62 :: c44:c45
hole_c46:c4721_62 :: c46:c47
hole_c6122_62 :: c61
hole_c4923_62 :: c49
hole_c51:c5224_62 :: c51:c52
hole_c53:c54:c55:c5625_62 :: c53:c54:c55:c56
hole_c58:c59:c6026_62 :: c58:c59:c60
hole_c16:c17:c18:c1927_62 :: c16:c17:c18:c19
hole_c20:c21:c22:c2328_62 :: c20:c21:c22:c23
hole_c14:c1529_62 :: c14:c15
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62 :: Nat -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
gen_c:c1:c2:c3:c431_62 :: Nat -> c:c1:c2:c3:c4
gen_c14:c1532_62 :: Nat -> c14:c15


Lemmas:
appendreverse#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n250_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n250_62, b)), rt in Omega(0)


Generator Equations:
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0) <=> nil
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(x, 1)) <=> ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(x))
gen_c:c1:c2:c3:c431_62(0) <=> c
gen_c:c1:c2:c3:c431_62(+(x, 1)) <=> c2(c16, gen_c:c1:c2:c3:c431_62(x))
gen_c14:c1532_62(0) <=> c14
gen_c14:c1532_62(+(x, 1)) <=> c15(c, gen_c14:c1532_62(x))


The following defined symbols remain to be analysed:
LINEMULT#1, APPENDREVERSE, APPENDREVERSE#1, BFTMULT', BFTMULT'#1, matrixMult, MATRIXMULT, COMPUTELINE, COMPUTELINE#1, lineMult, LINEMULT, MATRIXMULT#1, bftMult', bftMult'#1, computeLine, computeLine#1, lineMult#1, matrixMult#1

They will be analysed ascendingly in the following order:
APPENDREVERSE = APPENDREVERSE#1
BFTMULT' = BFTMULT'#1
matrixMult < BFTMULT'#1
MATRIXMULT < BFTMULT'#1
matrixMult < bftMult'#1
matrixMult = matrixMult#1
MATRIXMULT = MATRIXMULT#1
COMPUTELINE = COMPUTELINE#1
COMPUTELINE < MATRIXMULT#1
lineMult < COMPUTELINE#1
LINEMULT < COMPUTELINE#1
lineMult < computeLine#1
lineMult = lineMult#1
LINEMULT = LINEMULT#1
bftMult' = bftMult'#1
computeLine = computeLine#1
computeLine < matrixMult#1

----------------------------------------

(18) LowerBoundPropagationProof (FINISHED)
Propagated lower bound.
----------------------------------------

(19)
BOUNDS(n^1, INF)

----------------------------------------

(20)
Obligation:
Innermost TRS:
Rules:
*'(z0, z1) -> c24(#MULT(z0, z1))
+'(z0, z1) -> c25(#ADD(z0, z1))
APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
APPENDREVERSE#1(nil, z0) -> c28
BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
BFTMULT'#3(nil, z0, z1) -> c34
BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
COMPUTELINE#1(nil, z0, z1) -> c40
COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
COMPUTELINE#2(nil, z0, z1, z2) -> c42
DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
DEQUEUE#1(::(z0, z1), z2) -> c44
DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
DEQUEUE#2(::(z0, z1)) -> c46
DEQUEUE#2(nil) -> c47
ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
LINEMULT#1(nil, z0, z1) -> c52
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*'(z3, z2), z0), *'(z3, z2))
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
MATRIXMULT#1(nil, z0) -> c60
REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))
#ADD(#0, z0) -> c
#ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
#ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
#ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#MULT(#0, #0) -> c5
#MULT(#0, #neg(z0)) -> c6
#MULT(#0, #pos(z0)) -> c7
#MULT(#neg(z0), #0) -> c8
#MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
#MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
#MULT(#pos(z0), #0) -> c11
#MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
#MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
#NATMULT(#0, z0) -> c14
#NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
#PRED(#0) -> c16
#PRED(#neg(#s(z0))) -> c17
#PRED(#pos(#s(#0))) -> c18
#PRED(#pos(#s(#s(z0)))) -> c19
#SUCC(#0) -> c20
#SUCC(#neg(#s(#0))) -> c21
#SUCC(#neg(#s(#s(z0)))) -> c22
#SUCC(#pos(#s(z0))) -> c23
#add(#0, z0) -> z0
#add(#neg(#s(#0)), z0) -> #pred(z0)
#add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
#add(#pos(#s(#0)), z0) -> #succ(z0)
#add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
#mult(#0, #0) -> #0
#mult(#0, #neg(z0)) -> #0
#mult(#0, #pos(z0)) -> #0
#mult(#neg(z0), #0) -> #0
#mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
#mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #0) -> #0
#mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
#natmult(#0, z0) -> #0
#natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
#pred(#0) -> #neg(#s(#0))
#pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
#pred(#pos(#s(#0))) -> #0
#pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
#succ(#0) -> #pos(#s(#0))
#succ(#neg(#s(#0))) -> #0
#succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
#succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
*'(z0, z1) -> #mult(z0, z1)
+'(z0, z1) -> #add(z0, z1)
appendreverse(z0, z1) -> appendreverse#1(z0, z1)
appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
appendreverse#1(nil, z0) -> z0
bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
bftMult'#3(nil, z0, z1) -> z0
bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
computeLine#1(nil, z0, z1) -> z0
computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
computeLine#2(nil, z0, z1, z2) -> nil
dequeue(z0, z1) -> dequeue#1(z0, z1)
dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
enqueue(z0, z1) -> enqueue#1(z1, z0)
enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
lineMult#1(nil, z0, z1) -> nil
lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+'(*'(z3, z2), z0), lineMult(z2, z4, z1))
lineMult#2(nil, z0, z1, z2) -> ::(*'(z1, z0), lineMult(z0, z2, nil))
matrixMult(z0, z1) -> matrixMult#1(z0, z1)
matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
matrixMult#1(nil, z0) -> nil
reverse(z0) -> appendreverse(z0, nil)

Types:
*' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c24 :: c5:c6:c7:c8:c9:c10:c11:c12:c13 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#MULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c5:c6:c7:c8:c9:c10:c11:c12:c13
+' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c25 :: c:c1:c2:c3:c4 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#ADD :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c:c1:c2:c3:c4
APPENDREVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c26
c26 :: c27:c28 -> c26
APPENDREVERSE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c27:c28
:: :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c27 :: c26 -> c27:c28
nil :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c28 :: c27:c28
BFTMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c29
c29 :: c30 -> c29
BFTMULT' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c30
tuple#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c30 :: c31 -> c32 -> c30
BFTMULT'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c31
bftMult'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
BFTMULT'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c32
c31 :: c33:c34 -> c31
BFTMULT'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c33:c34
c32 :: c43 -> c32
DEQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c43
c33 :: c35:c36 -> c33:c34
BFTMULT'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c35:c36
c34 :: c33:c34
leaf :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c35 :: c30 -> c35:c36
node :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c36 :: c37 -> c48 -> c48 -> c35:c36
BFTMULT'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c37
enqueue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
ENQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c48
c37 :: c30 -> c57 -> c37
matrixMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
MATRIXMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c57
COMPUTELINE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c38
c38 :: c39:c40 -> c38
COMPUTELINE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c39:c40
c39 :: c41:c42 -> c39:c40
COMPUTELINE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c41:c42
c40 :: c39:c40
c41 :: c38 -> c50 -> c41:c42
lineMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
LINEMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c50
c42 :: c41:c42
c43 :: c44:c45 -> c43
DEQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c44:c45
c44 :: c44:c45
c45 :: c46:c47 -> c61 -> c44:c45
DEQUEUE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c46:c47
reverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
REVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c61
c46 :: c46:c47
c47 :: c46:c47
c48 :: c49 -> c48
ENQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c49
c49 :: c49
c50 :: c51:c52 -> c50
LINEMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c51:c52
c51 :: c53:c54:c55:c56 -> c51:c52
LINEMULT#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c52 :: c51:c52
c53 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c54 :: c50 -> c53:c54:c55:c56
c55 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c56 :: c50 -> c53:c54:c55:c56
c57 :: c58:c59:c60 -> c57
MATRIXMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c58:c59:c60
c58 :: c38 -> c58:c59:c60
c59 :: c57 -> c58:c59:c60
c60 :: c58:c59:c60
c61 :: c26 -> c61
#0 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c :: c:c1:c2:c3:c4
#neg :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#s :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c1 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4
#PRED :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c16:c17:c18:c19
c2 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
#add :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#pos :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c3 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4
#SUCC :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c20:c21:c22:c23
c4 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
c5 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c6 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c7 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c8 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c9 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
#NATMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c14:c15
c10 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c11 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c12 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c13 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c14 :: c14:c15
c15 :: c:c1:c2:c3:c4 -> c14:c15 -> c14:c15
#natmult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c16 :: c16:c17:c18:c19
c17 :: c16:c17:c18:c19
c18 :: c16:c17:c18:c19
c19 :: c16:c17:c18:c19
c20 :: c20:c21:c22:c23
c21 :: c20:c21:c22:c23
c22 :: c20:c21:c22:c23
c23 :: c20:c21:c22:c23
#pred :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#succ :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#mult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
enqueue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
matrixMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos1_62 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c5:c6:c7:c8:c9:c10:c11:c12:c132_62 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
hole_c:c1:c2:c3:c43_62 :: c:c1:c2:c3:c4
hole_c264_62 :: c26
hole_c27:c285_62 :: c27:c28
hole_c296_62 :: c29
hole_c307_62 :: c30
hole_c318_62 :: c31
hole_c329_62 :: c32
hole_c33:c3410_62 :: c33:c34
hole_c4311_62 :: c43
hole_c35:c3612_62 :: c35:c36
hole_c3713_62 :: c37
hole_c4814_62 :: c48
hole_c5715_62 :: c57
hole_c3816_62 :: c38
hole_c39:c4017_62 :: c39:c40
hole_c41:c4218_62 :: c41:c42
hole_c5019_62 :: c50
hole_c44:c4520_62 :: c44:c45
hole_c46:c4721_62 :: c46:c47
hole_c6122_62 :: c61
hole_c4923_62 :: c49
hole_c51:c5224_62 :: c51:c52
hole_c53:c54:c55:c5625_62 :: c53:c54:c55:c56
hole_c58:c59:c6026_62 :: c58:c59:c60
hole_c16:c17:c18:c1927_62 :: c16:c17:c18:c19
hole_c20:c21:c22:c2328_62 :: c20:c21:c22:c23
hole_c14:c1529_62 :: c14:c15
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62 :: Nat -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
gen_c:c1:c2:c3:c431_62 :: Nat -> c:c1:c2:c3:c4
gen_c14:c1532_62 :: Nat -> c14:c15


Lemmas:
appendreverse#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n250_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n250_62, b)), rt in Omega(0)
LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n4238_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n4238_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n4238_62)


Generator Equations:
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0) <=> nil
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(x, 1)) <=> ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(x))
gen_c:c1:c2:c3:c431_62(0) <=> c
gen_c:c1:c2:c3:c431_62(+(x, 1)) <=> c2(c16, gen_c:c1:c2:c3:c431_62(x))
gen_c14:c1532_62(0) <=> c14
gen_c14:c1532_62(+(x, 1)) <=> c15(c, gen_c14:c1532_62(x))


The following defined symbols remain to be analysed:
LINEMULT, APPENDREVERSE, APPENDREVERSE#1, BFTMULT', BFTMULT'#1, matrixMult, MATRIXMULT, COMPUTELINE, COMPUTELINE#1, lineMult, MATRIXMULT#1, bftMult', bftMult'#1, computeLine, computeLine#1, lineMult#1, matrixMult#1

They will be analysed ascendingly in the following order:
APPENDREVERSE = APPENDREVERSE#1
BFTMULT' = BFTMULT'#1
matrixMult < BFTMULT'#1
MATRIXMULT < BFTMULT'#1
matrixMult < bftMult'#1
matrixMult = matrixMult#1
MATRIXMULT = MATRIXMULT#1
COMPUTELINE = COMPUTELINE#1
COMPUTELINE < MATRIXMULT#1
lineMult < COMPUTELINE#1
LINEMULT < COMPUTELINE#1
lineMult < computeLine#1
lineMult = lineMult#1
LINEMULT = LINEMULT#1
bftMult' = bftMult'#1
computeLine = computeLine#1
computeLine < matrixMult#1

----------------------------------------

(21) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
LINEMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62)) -> *33_62, rt in Omega(n30296_62)

Induction Base:
LINEMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0))

Induction Step:
LINEMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n30296_62, 1)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n30296_62, 1))) ->_R^Omega(1)
c50(LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n30296_62, 1)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n30296_62, 1)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a))) ->_R^Omega(1)
c50(c51(LINEMULT#2(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n30296_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62)))) ->_R^Omega(1)
c50(c51(c54(LINEMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62))))) ->_IH
c50(c51(c54(*33_62)))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(22)
Obligation:
Innermost TRS:
Rules:
*'(z0, z1) -> c24(#MULT(z0, z1))
+'(z0, z1) -> c25(#ADD(z0, z1))
APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
APPENDREVERSE#1(nil, z0) -> c28
BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
BFTMULT'#3(nil, z0, z1) -> c34
BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
COMPUTELINE#1(nil, z0, z1) -> c40
COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
COMPUTELINE#2(nil, z0, z1, z2) -> c42
DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
DEQUEUE#1(::(z0, z1), z2) -> c44
DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
DEQUEUE#2(::(z0, z1)) -> c46
DEQUEUE#2(nil) -> c47
ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
LINEMULT#1(nil, z0, z1) -> c52
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*'(z3, z2), z0), *'(z3, z2))
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
MATRIXMULT#1(nil, z0) -> c60
REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))
#ADD(#0, z0) -> c
#ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
#ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
#ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#MULT(#0, #0) -> c5
#MULT(#0, #neg(z0)) -> c6
#MULT(#0, #pos(z0)) -> c7
#MULT(#neg(z0), #0) -> c8
#MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
#MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
#MULT(#pos(z0), #0) -> c11
#MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
#MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
#NATMULT(#0, z0) -> c14
#NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
#PRED(#0) -> c16
#PRED(#neg(#s(z0))) -> c17
#PRED(#pos(#s(#0))) -> c18
#PRED(#pos(#s(#s(z0)))) -> c19
#SUCC(#0) -> c20
#SUCC(#neg(#s(#0))) -> c21
#SUCC(#neg(#s(#s(z0)))) -> c22
#SUCC(#pos(#s(z0))) -> c23
#add(#0, z0) -> z0
#add(#neg(#s(#0)), z0) -> #pred(z0)
#add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
#add(#pos(#s(#0)), z0) -> #succ(z0)
#add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
#mult(#0, #0) -> #0
#mult(#0, #neg(z0)) -> #0
#mult(#0, #pos(z0)) -> #0
#mult(#neg(z0), #0) -> #0
#mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
#mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #0) -> #0
#mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
#natmult(#0, z0) -> #0
#natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
#pred(#0) -> #neg(#s(#0))
#pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
#pred(#pos(#s(#0))) -> #0
#pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
#succ(#0) -> #pos(#s(#0))
#succ(#neg(#s(#0))) -> #0
#succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
#succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
*'(z0, z1) -> #mult(z0, z1)
+'(z0, z1) -> #add(z0, z1)
appendreverse(z0, z1) -> appendreverse#1(z0, z1)
appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
appendreverse#1(nil, z0) -> z0
bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
bftMult'#3(nil, z0, z1) -> z0
bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
computeLine#1(nil, z0, z1) -> z0
computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
computeLine#2(nil, z0, z1, z2) -> nil
dequeue(z0, z1) -> dequeue#1(z0, z1)
dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
enqueue(z0, z1) -> enqueue#1(z1, z0)
enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
lineMult#1(nil, z0, z1) -> nil
lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+'(*'(z3, z2), z0), lineMult(z2, z4, z1))
lineMult#2(nil, z0, z1, z2) -> ::(*'(z1, z0), lineMult(z0, z2, nil))
matrixMult(z0, z1) -> matrixMult#1(z0, z1)
matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
matrixMult#1(nil, z0) -> nil
reverse(z0) -> appendreverse(z0, nil)

Types:
*' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c24 :: c5:c6:c7:c8:c9:c10:c11:c12:c13 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#MULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c5:c6:c7:c8:c9:c10:c11:c12:c13
+' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c25 :: c:c1:c2:c3:c4 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#ADD :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c:c1:c2:c3:c4
APPENDREVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c26
c26 :: c27:c28 -> c26
APPENDREVERSE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c27:c28
:: :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c27 :: c26 -> c27:c28
nil :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c28 :: c27:c28
BFTMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c29
c29 :: c30 -> c29
BFTMULT' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c30
tuple#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c30 :: c31 -> c32 -> c30
BFTMULT'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c31
bftMult'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
BFTMULT'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c32
c31 :: c33:c34 -> c31
BFTMULT'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c33:c34
c32 :: c43 -> c32
DEQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c43
c33 :: c35:c36 -> c33:c34
BFTMULT'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c35:c36
c34 :: c33:c34
leaf :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c35 :: c30 -> c35:c36
node :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c36 :: c37 -> c48 -> c48 -> c35:c36
BFTMULT'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c37
enqueue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
ENQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c48
c37 :: c30 -> c57 -> c37
matrixMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
MATRIXMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c57
COMPUTELINE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c38
c38 :: c39:c40 -> c38
COMPUTELINE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c39:c40
c39 :: c41:c42 -> c39:c40
COMPUTELINE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c41:c42
c40 :: c39:c40
c41 :: c38 -> c50 -> c41:c42
lineMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
LINEMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c50
c42 :: c41:c42
c43 :: c44:c45 -> c43
DEQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c44:c45
c44 :: c44:c45
c45 :: c46:c47 -> c61 -> c44:c45
DEQUEUE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c46:c47
reverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
REVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c61
c46 :: c46:c47
c47 :: c46:c47
c48 :: c49 -> c48
ENQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c49
c49 :: c49
c50 :: c51:c52 -> c50
LINEMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c51:c52
c51 :: c53:c54:c55:c56 -> c51:c52
LINEMULT#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c52 :: c51:c52
c53 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c54 :: c50 -> c53:c54:c55:c56
c55 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c56 :: c50 -> c53:c54:c55:c56
c57 :: c58:c59:c60 -> c57
MATRIXMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c58:c59:c60
c58 :: c38 -> c58:c59:c60
c59 :: c57 -> c58:c59:c60
c60 :: c58:c59:c60
c61 :: c26 -> c61
#0 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c :: c:c1:c2:c3:c4
#neg :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#s :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c1 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4
#PRED :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c16:c17:c18:c19
c2 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
#add :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#pos :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c3 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4
#SUCC :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c20:c21:c22:c23
c4 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
c5 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c6 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c7 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c8 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c9 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
#NATMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c14:c15
c10 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c11 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c12 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c13 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c14 :: c14:c15
c15 :: c:c1:c2:c3:c4 -> c14:c15 -> c14:c15
#natmult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c16 :: c16:c17:c18:c19
c17 :: c16:c17:c18:c19
c18 :: c16:c17:c18:c19
c19 :: c16:c17:c18:c19
c20 :: c20:c21:c22:c23
c21 :: c20:c21:c22:c23
c22 :: c20:c21:c22:c23
c23 :: c20:c21:c22:c23
#pred :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#succ :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#mult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
enqueue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
matrixMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos1_62 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c5:c6:c7:c8:c9:c10:c11:c12:c132_62 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
hole_c:c1:c2:c3:c43_62 :: c:c1:c2:c3:c4
hole_c264_62 :: c26
hole_c27:c285_62 :: c27:c28
hole_c296_62 :: c29
hole_c307_62 :: c30
hole_c318_62 :: c31
hole_c329_62 :: c32
hole_c33:c3410_62 :: c33:c34
hole_c4311_62 :: c43
hole_c35:c3612_62 :: c35:c36
hole_c3713_62 :: c37
hole_c4814_62 :: c48
hole_c5715_62 :: c57
hole_c3816_62 :: c38
hole_c39:c4017_62 :: c39:c40
hole_c41:c4218_62 :: c41:c42
hole_c5019_62 :: c50
hole_c44:c4520_62 :: c44:c45
hole_c46:c4721_62 :: c46:c47
hole_c6122_62 :: c61
hole_c4923_62 :: c49
hole_c51:c5224_62 :: c51:c52
hole_c53:c54:c55:c5625_62 :: c53:c54:c55:c56
hole_c58:c59:c6026_62 :: c58:c59:c60
hole_c16:c17:c18:c1927_62 :: c16:c17:c18:c19
hole_c20:c21:c22:c2328_62 :: c20:c21:c22:c23
hole_c14:c1529_62 :: c14:c15
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62 :: Nat -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
gen_c:c1:c2:c3:c431_62 :: Nat -> c:c1:c2:c3:c4
gen_c14:c1532_62 :: Nat -> c14:c15


Lemmas:
appendreverse#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n250_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n250_62, b)), rt in Omega(0)
LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n4238_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n4238_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n4238_62)
LINEMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62)) -> *33_62, rt in Omega(n30296_62)


Generator Equations:
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0) <=> nil
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(x, 1)) <=> ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(x))
gen_c:c1:c2:c3:c431_62(0) <=> c
gen_c:c1:c2:c3:c431_62(+(x, 1)) <=> c2(c16, gen_c:c1:c2:c3:c431_62(x))
gen_c14:c1532_62(0) <=> c14
gen_c14:c1532_62(+(x, 1)) <=> c15(c, gen_c14:c1532_62(x))


The following defined symbols remain to be analysed:
LINEMULT#1, APPENDREVERSE, APPENDREVERSE#1, BFTMULT', BFTMULT'#1, matrixMult, MATRIXMULT, COMPUTELINE, COMPUTELINE#1, lineMult, MATRIXMULT#1, bftMult', bftMult'#1, computeLine, computeLine#1, lineMult#1, matrixMult#1

They will be analysed ascendingly in the following order:
APPENDREVERSE = APPENDREVERSE#1
BFTMULT' = BFTMULT'#1
matrixMult < BFTMULT'#1
MATRIXMULT < BFTMULT'#1
matrixMult < bftMult'#1
matrixMult = matrixMult#1
MATRIXMULT = MATRIXMULT#1
COMPUTELINE = COMPUTELINE#1
COMPUTELINE < MATRIXMULT#1
lineMult < COMPUTELINE#1
LINEMULT < COMPUTELINE#1
lineMult < computeLine#1
lineMult = lineMult#1
LINEMULT = LINEMULT#1
bftMult' = bftMult'#1
computeLine = computeLine#1
computeLine < matrixMult#1

----------------------------------------

(23) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n60901_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n60901_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n60901_62)

Induction Base:
LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, 0)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c))

Induction Step:
LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, +(n60901_62, 1))), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n60901_62, 1)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) ->_R^Omega(1)
c51(LINEMULT#2(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n60901_62, 1)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c), nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n60901_62)))) ->_R^Omega(1)
c51(c54(LINEMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n60901_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n60901_62)))) ->_R^Omega(1)
c51(c54(c50(LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n60901_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n60901_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c))))) ->_IH
c51(c54(c50(*33_62)))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(24)
Obligation:
Innermost TRS:
Rules:
*'(z0, z1) -> c24(#MULT(z0, z1))
+'(z0, z1) -> c25(#ADD(z0, z1))
APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
APPENDREVERSE#1(nil, z0) -> c28
BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
BFTMULT'#3(nil, z0, z1) -> c34
BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
COMPUTELINE#1(nil, z0, z1) -> c40
COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
COMPUTELINE#2(nil, z0, z1, z2) -> c42
DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
DEQUEUE#1(::(z0, z1), z2) -> c44
DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
DEQUEUE#2(::(z0, z1)) -> c46
DEQUEUE#2(nil) -> c47
ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
LINEMULT#1(nil, z0, z1) -> c52
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*'(z3, z2), z0), *'(z3, z2))
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
MATRIXMULT#1(nil, z0) -> c60
REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))
#ADD(#0, z0) -> c
#ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
#ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
#ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#MULT(#0, #0) -> c5
#MULT(#0, #neg(z0)) -> c6
#MULT(#0, #pos(z0)) -> c7
#MULT(#neg(z0), #0) -> c8
#MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
#MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
#MULT(#pos(z0), #0) -> c11
#MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
#MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
#NATMULT(#0, z0) -> c14
#NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
#PRED(#0) -> c16
#PRED(#neg(#s(z0))) -> c17
#PRED(#pos(#s(#0))) -> c18
#PRED(#pos(#s(#s(z0)))) -> c19
#SUCC(#0) -> c20
#SUCC(#neg(#s(#0))) -> c21
#SUCC(#neg(#s(#s(z0)))) -> c22
#SUCC(#pos(#s(z0))) -> c23
#add(#0, z0) -> z0
#add(#neg(#s(#0)), z0) -> #pred(z0)
#add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
#add(#pos(#s(#0)), z0) -> #succ(z0)
#add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
#mult(#0, #0) -> #0
#mult(#0, #neg(z0)) -> #0
#mult(#0, #pos(z0)) -> #0
#mult(#neg(z0), #0) -> #0
#mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
#mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #0) -> #0
#mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
#natmult(#0, z0) -> #0
#natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
#pred(#0) -> #neg(#s(#0))
#pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
#pred(#pos(#s(#0))) -> #0
#pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
#succ(#0) -> #pos(#s(#0))
#succ(#neg(#s(#0))) -> #0
#succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
#succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
*'(z0, z1) -> #mult(z0, z1)
+'(z0, z1) -> #add(z0, z1)
appendreverse(z0, z1) -> appendreverse#1(z0, z1)
appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
appendreverse#1(nil, z0) -> z0
bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
bftMult'#3(nil, z0, z1) -> z0
bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
computeLine#1(nil, z0, z1) -> z0
computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
computeLine#2(nil, z0, z1, z2) -> nil
dequeue(z0, z1) -> dequeue#1(z0, z1)
dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
enqueue(z0, z1) -> enqueue#1(z1, z0)
enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
lineMult#1(nil, z0, z1) -> nil
lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+'(*'(z3, z2), z0), lineMult(z2, z4, z1))
lineMult#2(nil, z0, z1, z2) -> ::(*'(z1, z0), lineMult(z0, z2, nil))
matrixMult(z0, z1) -> matrixMult#1(z0, z1)
matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
matrixMult#1(nil, z0) -> nil
reverse(z0) -> appendreverse(z0, nil)

Types:
*' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c24 :: c5:c6:c7:c8:c9:c10:c11:c12:c13 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#MULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c5:c6:c7:c8:c9:c10:c11:c12:c13
+' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c25 :: c:c1:c2:c3:c4 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#ADD :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c:c1:c2:c3:c4
APPENDREVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c26
c26 :: c27:c28 -> c26
APPENDREVERSE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c27:c28
:: :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c27 :: c26 -> c27:c28
nil :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c28 :: c27:c28
BFTMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c29
c29 :: c30 -> c29
BFTMULT' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c30
tuple#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c30 :: c31 -> c32 -> c30
BFTMULT'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c31
bftMult'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
BFTMULT'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c32
c31 :: c33:c34 -> c31
BFTMULT'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c33:c34
c32 :: c43 -> c32
DEQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c43
c33 :: c35:c36 -> c33:c34
BFTMULT'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c35:c36
c34 :: c33:c34
leaf :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c35 :: c30 -> c35:c36
node :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c36 :: c37 -> c48 -> c48 -> c35:c36
BFTMULT'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c37
enqueue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
ENQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c48
c37 :: c30 -> c57 -> c37
matrixMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
MATRIXMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c57
COMPUTELINE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c38
c38 :: c39:c40 -> c38
COMPUTELINE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c39:c40
c39 :: c41:c42 -> c39:c40
COMPUTELINE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c41:c42
c40 :: c39:c40
c41 :: c38 -> c50 -> c41:c42
lineMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
LINEMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c50
c42 :: c41:c42
c43 :: c44:c45 -> c43
DEQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c44:c45
c44 :: c44:c45
c45 :: c46:c47 -> c61 -> c44:c45
DEQUEUE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c46:c47
reverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
REVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c61
c46 :: c46:c47
c47 :: c46:c47
c48 :: c49 -> c48
ENQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c49
c49 :: c49
c50 :: c51:c52 -> c50
LINEMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c51:c52
c51 :: c53:c54:c55:c56 -> c51:c52
LINEMULT#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c52 :: c51:c52
c53 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c54 :: c50 -> c53:c54:c55:c56
c55 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c56 :: c50 -> c53:c54:c55:c56
c57 :: c58:c59:c60 -> c57
MATRIXMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c58:c59:c60
c58 :: c38 -> c58:c59:c60
c59 :: c57 -> c58:c59:c60
c60 :: c58:c59:c60
c61 :: c26 -> c61
#0 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c :: c:c1:c2:c3:c4
#neg :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#s :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c1 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4
#PRED :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c16:c17:c18:c19
c2 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
#add :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#pos :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c3 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4
#SUCC :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c20:c21:c22:c23
c4 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
c5 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c6 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c7 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c8 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c9 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
#NATMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c14:c15
c10 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c11 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c12 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c13 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c14 :: c14:c15
c15 :: c:c1:c2:c3:c4 -> c14:c15 -> c14:c15
#natmult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c16 :: c16:c17:c18:c19
c17 :: c16:c17:c18:c19
c18 :: c16:c17:c18:c19
c19 :: c16:c17:c18:c19
c20 :: c20:c21:c22:c23
c21 :: c20:c21:c22:c23
c22 :: c20:c21:c22:c23
c23 :: c20:c21:c22:c23
#pred :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#succ :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#mult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
enqueue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
matrixMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos1_62 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c5:c6:c7:c8:c9:c10:c11:c12:c132_62 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
hole_c:c1:c2:c3:c43_62 :: c:c1:c2:c3:c4
hole_c264_62 :: c26
hole_c27:c285_62 :: c27:c28
hole_c296_62 :: c29
hole_c307_62 :: c30
hole_c318_62 :: c31
hole_c329_62 :: c32
hole_c33:c3410_62 :: c33:c34
hole_c4311_62 :: c43
hole_c35:c3612_62 :: c35:c36
hole_c3713_62 :: c37
hole_c4814_62 :: c48
hole_c5715_62 :: c57
hole_c3816_62 :: c38
hole_c39:c4017_62 :: c39:c40
hole_c41:c4218_62 :: c41:c42
hole_c5019_62 :: c50
hole_c44:c4520_62 :: c44:c45
hole_c46:c4721_62 :: c46:c47
hole_c6122_62 :: c61
hole_c4923_62 :: c49
hole_c51:c5224_62 :: c51:c52
hole_c53:c54:c55:c5625_62 :: c53:c54:c55:c56
hole_c58:c59:c6026_62 :: c58:c59:c60
hole_c16:c17:c18:c1927_62 :: c16:c17:c18:c19
hole_c20:c21:c22:c2328_62 :: c20:c21:c22:c23
hole_c14:c1529_62 :: c14:c15
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62 :: Nat -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
gen_c:c1:c2:c3:c431_62 :: Nat -> c:c1:c2:c3:c4
gen_c14:c1532_62 :: Nat -> c14:c15


Lemmas:
appendreverse#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n250_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n250_62, b)), rt in Omega(0)
LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n60901_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n60901_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n60901_62)
LINEMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62)) -> *33_62, rt in Omega(n30296_62)


Generator Equations:
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0) <=> nil
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(x, 1)) <=> ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(x))
gen_c:c1:c2:c3:c431_62(0) <=> c
gen_c:c1:c2:c3:c431_62(+(x, 1)) <=> c2(c16, gen_c:c1:c2:c3:c431_62(x))
gen_c14:c1532_62(0) <=> c14
gen_c14:c1532_62(+(x, 1)) <=> c15(c, gen_c14:c1532_62(x))


The following defined symbols remain to be analysed:
lineMult#1, APPENDREVERSE, APPENDREVERSE#1, BFTMULT', BFTMULT'#1, matrixMult, MATRIXMULT, COMPUTELINE, COMPUTELINE#1, lineMult, MATRIXMULT#1, bftMult', bftMult'#1, computeLine, computeLine#1, matrixMult#1

They will be analysed ascendingly in the following order:
APPENDREVERSE = APPENDREVERSE#1
BFTMULT' = BFTMULT'#1
matrixMult < BFTMULT'#1
MATRIXMULT < BFTMULT'#1
matrixMult < bftMult'#1
matrixMult = matrixMult#1
MATRIXMULT = MATRIXMULT#1
COMPUTELINE = COMPUTELINE#1
COMPUTELINE < MATRIXMULT#1
lineMult < COMPUTELINE#1
lineMult < computeLine#1
lineMult = lineMult#1
bftMult' = bftMult'#1
computeLine = computeLine#1
computeLine < matrixMult#1

----------------------------------------

(25) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
lineMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n94689_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n94689_62)

Induction Base:
lineMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, 0)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c))

Induction Step:
lineMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, +(n94689_62, 1))), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) ->_R^Omega(0)
lineMult#2(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c), nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n94689_62))) ->_R^Omega(0)
::(*'(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)), lineMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n94689_62)), nil)) ->_R^Omega(1)
::(c24(#MULT(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c))), lineMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n94689_62)), nil)) ->_R^Omega(0)
::(c24(#MULT(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c))), lineMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n94689_62)), nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c))) ->_IH
::(c24(#MULT(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c))), *33_62)

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(26)
Obligation:
Innermost TRS:
Rules:
*'(z0, z1) -> c24(#MULT(z0, z1))
+'(z0, z1) -> c25(#ADD(z0, z1))
APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
APPENDREVERSE#1(nil, z0) -> c28
BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
BFTMULT'#3(nil, z0, z1) -> c34
BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
COMPUTELINE#1(nil, z0, z1) -> c40
COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
COMPUTELINE#2(nil, z0, z1, z2) -> c42
DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
DEQUEUE#1(::(z0, z1), z2) -> c44
DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
DEQUEUE#2(::(z0, z1)) -> c46
DEQUEUE#2(nil) -> c47
ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
LINEMULT#1(nil, z0, z1) -> c52
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*'(z3, z2), z0), *'(z3, z2))
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
MATRIXMULT#1(nil, z0) -> c60
REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))
#ADD(#0, z0) -> c
#ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
#ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
#ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#MULT(#0, #0) -> c5
#MULT(#0, #neg(z0)) -> c6
#MULT(#0, #pos(z0)) -> c7
#MULT(#neg(z0), #0) -> c8
#MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
#MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
#MULT(#pos(z0), #0) -> c11
#MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
#MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
#NATMULT(#0, z0) -> c14
#NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
#PRED(#0) -> c16
#PRED(#neg(#s(z0))) -> c17
#PRED(#pos(#s(#0))) -> c18
#PRED(#pos(#s(#s(z0)))) -> c19
#SUCC(#0) -> c20
#SUCC(#neg(#s(#0))) -> c21
#SUCC(#neg(#s(#s(z0)))) -> c22
#SUCC(#pos(#s(z0))) -> c23
#add(#0, z0) -> z0
#add(#neg(#s(#0)), z0) -> #pred(z0)
#add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
#add(#pos(#s(#0)), z0) -> #succ(z0)
#add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
#mult(#0, #0) -> #0
#mult(#0, #neg(z0)) -> #0
#mult(#0, #pos(z0)) -> #0
#mult(#neg(z0), #0) -> #0
#mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
#mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #0) -> #0
#mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
#natmult(#0, z0) -> #0
#natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
#pred(#0) -> #neg(#s(#0))
#pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
#pred(#pos(#s(#0))) -> #0
#pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
#succ(#0) -> #pos(#s(#0))
#succ(#neg(#s(#0))) -> #0
#succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
#succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
*'(z0, z1) -> #mult(z0, z1)
+'(z0, z1) -> #add(z0, z1)
appendreverse(z0, z1) -> appendreverse#1(z0, z1)
appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
appendreverse#1(nil, z0) -> z0
bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
bftMult'#3(nil, z0, z1) -> z0
bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
computeLine#1(nil, z0, z1) -> z0
computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
computeLine#2(nil, z0, z1, z2) -> nil
dequeue(z0, z1) -> dequeue#1(z0, z1)
dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
enqueue(z0, z1) -> enqueue#1(z1, z0)
enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
lineMult#1(nil, z0, z1) -> nil
lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+'(*'(z3, z2), z0), lineMult(z2, z4, z1))
lineMult#2(nil, z0, z1, z2) -> ::(*'(z1, z0), lineMult(z0, z2, nil))
matrixMult(z0, z1) -> matrixMult#1(z0, z1)
matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
matrixMult#1(nil, z0) -> nil
reverse(z0) -> appendreverse(z0, nil)

Types:
*' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c24 :: c5:c6:c7:c8:c9:c10:c11:c12:c13 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#MULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c5:c6:c7:c8:c9:c10:c11:c12:c13
+' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c25 :: c:c1:c2:c3:c4 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#ADD :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c:c1:c2:c3:c4
APPENDREVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c26
c26 :: c27:c28 -> c26
APPENDREVERSE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c27:c28
:: :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c27 :: c26 -> c27:c28
nil :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c28 :: c27:c28
BFTMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c29
c29 :: c30 -> c29
BFTMULT' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c30
tuple#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c30 :: c31 -> c32 -> c30
BFTMULT'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c31
bftMult'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
BFTMULT'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c32
c31 :: c33:c34 -> c31
BFTMULT'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c33:c34
c32 :: c43 -> c32
DEQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c43
c33 :: c35:c36 -> c33:c34
BFTMULT'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c35:c36
c34 :: c33:c34
leaf :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c35 :: c30 -> c35:c36
node :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c36 :: c37 -> c48 -> c48 -> c35:c36
BFTMULT'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c37
enqueue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
ENQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c48
c37 :: c30 -> c57 -> c37
matrixMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
MATRIXMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c57
COMPUTELINE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c38
c38 :: c39:c40 -> c38
COMPUTELINE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c39:c40
c39 :: c41:c42 -> c39:c40
COMPUTELINE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c41:c42
c40 :: c39:c40
c41 :: c38 -> c50 -> c41:c42
lineMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
LINEMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c50
c42 :: c41:c42
c43 :: c44:c45 -> c43
DEQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c44:c45
c44 :: c44:c45
c45 :: c46:c47 -> c61 -> c44:c45
DEQUEUE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c46:c47
reverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
REVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c61
c46 :: c46:c47
c47 :: c46:c47
c48 :: c49 -> c48
ENQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c49
c49 :: c49
c50 :: c51:c52 -> c50
LINEMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c51:c52
c51 :: c53:c54:c55:c56 -> c51:c52
LINEMULT#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c52 :: c51:c52
c53 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c54 :: c50 -> c53:c54:c55:c56
c55 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c56 :: c50 -> c53:c54:c55:c56
c57 :: c58:c59:c60 -> c57
MATRIXMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c58:c59:c60
c58 :: c38 -> c58:c59:c60
c59 :: c57 -> c58:c59:c60
c60 :: c58:c59:c60
c61 :: c26 -> c61
#0 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c :: c:c1:c2:c3:c4
#neg :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#s :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c1 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4
#PRED :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c16:c17:c18:c19
c2 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
#add :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#pos :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c3 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4
#SUCC :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c20:c21:c22:c23
c4 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
c5 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c6 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c7 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c8 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c9 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
#NATMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c14:c15
c10 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c11 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c12 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c13 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c14 :: c14:c15
c15 :: c:c1:c2:c3:c4 -> c14:c15 -> c14:c15
#natmult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c16 :: c16:c17:c18:c19
c17 :: c16:c17:c18:c19
c18 :: c16:c17:c18:c19
c19 :: c16:c17:c18:c19
c20 :: c20:c21:c22:c23
c21 :: c20:c21:c22:c23
c22 :: c20:c21:c22:c23
c23 :: c20:c21:c22:c23
#pred :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#succ :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#mult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
enqueue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
matrixMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos1_62 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c5:c6:c7:c8:c9:c10:c11:c12:c132_62 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
hole_c:c1:c2:c3:c43_62 :: c:c1:c2:c3:c4
hole_c264_62 :: c26
hole_c27:c285_62 :: c27:c28
hole_c296_62 :: c29
hole_c307_62 :: c30
hole_c318_62 :: c31
hole_c329_62 :: c32
hole_c33:c3410_62 :: c33:c34
hole_c4311_62 :: c43
hole_c35:c3612_62 :: c35:c36
hole_c3713_62 :: c37
hole_c4814_62 :: c48
hole_c5715_62 :: c57
hole_c3816_62 :: c38
hole_c39:c4017_62 :: c39:c40
hole_c41:c4218_62 :: c41:c42
hole_c5019_62 :: c50
hole_c44:c4520_62 :: c44:c45
hole_c46:c4721_62 :: c46:c47
hole_c6122_62 :: c61
hole_c4923_62 :: c49
hole_c51:c5224_62 :: c51:c52
hole_c53:c54:c55:c5625_62 :: c53:c54:c55:c56
hole_c58:c59:c6026_62 :: c58:c59:c60
hole_c16:c17:c18:c1927_62 :: c16:c17:c18:c19
hole_c20:c21:c22:c2328_62 :: c20:c21:c22:c23
hole_c14:c1529_62 :: c14:c15
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62 :: Nat -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
gen_c:c1:c2:c3:c431_62 :: Nat -> c:c1:c2:c3:c4
gen_c14:c1532_62 :: Nat -> c14:c15


Lemmas:
appendreverse#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n250_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n250_62, b)), rt in Omega(0)
LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n60901_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n60901_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n60901_62)
LINEMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62)) -> *33_62, rt in Omega(n30296_62)
lineMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n94689_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n94689_62)


Generator Equations:
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0) <=> nil
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(x, 1)) <=> ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(x))
gen_c:c1:c2:c3:c431_62(0) <=> c
gen_c:c1:c2:c3:c431_62(+(x, 1)) <=> c2(c16, gen_c:c1:c2:c3:c431_62(x))
gen_c14:c1532_62(0) <=> c14
gen_c14:c1532_62(+(x, 1)) <=> c15(c, gen_c14:c1532_62(x))


The following defined symbols remain to be analysed:
lineMult, APPENDREVERSE, APPENDREVERSE#1, BFTMULT', BFTMULT'#1, matrixMult, MATRIXMULT, COMPUTELINE, COMPUTELINE#1, MATRIXMULT#1, bftMult', bftMult'#1, computeLine, computeLine#1, matrixMult#1

They will be analysed ascendingly in the following order:
APPENDREVERSE = APPENDREVERSE#1
BFTMULT' = BFTMULT'#1
matrixMult < BFTMULT'#1
MATRIXMULT < BFTMULT'#1
matrixMult < bftMult'#1
matrixMult = matrixMult#1
MATRIXMULT = MATRIXMULT#1
COMPUTELINE = COMPUTELINE#1
COMPUTELINE < MATRIXMULT#1
lineMult < COMPUTELINE#1
lineMult < computeLine#1
lineMult = lineMult#1
bftMult' = bftMult'#1
computeLine = computeLine#1
computeLine < matrixMult#1

----------------------------------------

(27) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
lineMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n4908489_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0)) -> *33_62, rt in Omega(n4908489_62)

Induction Base:
lineMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0))

Induction Step:
lineMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n4908489_62, 1)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0)) ->_R^Omega(0)
lineMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n4908489_62, 1)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a)) ->_R^Omega(0)
lineMult#2(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n4908489_62)) ->_R^Omega(0)
::(*'(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a)), lineMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n4908489_62), nil)) ->_R^Omega(1)
::(c24(#MULT(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a))), lineMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n4908489_62), nil)) ->_IH
::(c24(#MULT(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a))), *33_62)

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(28)
Obligation:
Innermost TRS:
Rules:
*'(z0, z1) -> c24(#MULT(z0, z1))
+'(z0, z1) -> c25(#ADD(z0, z1))
APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
APPENDREVERSE#1(nil, z0) -> c28
BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
BFTMULT'#3(nil, z0, z1) -> c34
BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
COMPUTELINE#1(nil, z0, z1) -> c40
COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
COMPUTELINE#2(nil, z0, z1, z2) -> c42
DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
DEQUEUE#1(::(z0, z1), z2) -> c44
DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
DEQUEUE#2(::(z0, z1)) -> c46
DEQUEUE#2(nil) -> c47
ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
LINEMULT#1(nil, z0, z1) -> c52
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*'(z3, z2), z0), *'(z3, z2))
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
MATRIXMULT#1(nil, z0) -> c60
REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))
#ADD(#0, z0) -> c
#ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
#ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
#ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#MULT(#0, #0) -> c5
#MULT(#0, #neg(z0)) -> c6
#MULT(#0, #pos(z0)) -> c7
#MULT(#neg(z0), #0) -> c8
#MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
#MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
#MULT(#pos(z0), #0) -> c11
#MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
#MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
#NATMULT(#0, z0) -> c14
#NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
#PRED(#0) -> c16
#PRED(#neg(#s(z0))) -> c17
#PRED(#pos(#s(#0))) -> c18
#PRED(#pos(#s(#s(z0)))) -> c19
#SUCC(#0) -> c20
#SUCC(#neg(#s(#0))) -> c21
#SUCC(#neg(#s(#s(z0)))) -> c22
#SUCC(#pos(#s(z0))) -> c23
#add(#0, z0) -> z0
#add(#neg(#s(#0)), z0) -> #pred(z0)
#add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
#add(#pos(#s(#0)), z0) -> #succ(z0)
#add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
#mult(#0, #0) -> #0
#mult(#0, #neg(z0)) -> #0
#mult(#0, #pos(z0)) -> #0
#mult(#neg(z0), #0) -> #0
#mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
#mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #0) -> #0
#mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
#natmult(#0, z0) -> #0
#natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
#pred(#0) -> #neg(#s(#0))
#pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
#pred(#pos(#s(#0))) -> #0
#pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
#succ(#0) -> #pos(#s(#0))
#succ(#neg(#s(#0))) -> #0
#succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
#succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
*'(z0, z1) -> #mult(z0, z1)
+'(z0, z1) -> #add(z0, z1)
appendreverse(z0, z1) -> appendreverse#1(z0, z1)
appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
appendreverse#1(nil, z0) -> z0
bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
bftMult'#3(nil, z0, z1) -> z0
bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
computeLine#1(nil, z0, z1) -> z0
computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
computeLine#2(nil, z0, z1, z2) -> nil
dequeue(z0, z1) -> dequeue#1(z0, z1)
dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
enqueue(z0, z1) -> enqueue#1(z1, z0)
enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
lineMult#1(nil, z0, z1) -> nil
lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+'(*'(z3, z2), z0), lineMult(z2, z4, z1))
lineMult#2(nil, z0, z1, z2) -> ::(*'(z1, z0), lineMult(z0, z2, nil))
matrixMult(z0, z1) -> matrixMult#1(z0, z1)
matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
matrixMult#1(nil, z0) -> nil
reverse(z0) -> appendreverse(z0, nil)

Types:
*' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c24 :: c5:c6:c7:c8:c9:c10:c11:c12:c13 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#MULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c5:c6:c7:c8:c9:c10:c11:c12:c13
+' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c25 :: c:c1:c2:c3:c4 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#ADD :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c:c1:c2:c3:c4
APPENDREVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c26
c26 :: c27:c28 -> c26
APPENDREVERSE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c27:c28
:: :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c27 :: c26 -> c27:c28
nil :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c28 :: c27:c28
BFTMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c29
c29 :: c30 -> c29
BFTMULT' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c30
tuple#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c30 :: c31 -> c32 -> c30
BFTMULT'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c31
bftMult'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
BFTMULT'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c32
c31 :: c33:c34 -> c31
BFTMULT'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c33:c34
c32 :: c43 -> c32
DEQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c43
c33 :: c35:c36 -> c33:c34
BFTMULT'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c35:c36
c34 :: c33:c34
leaf :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c35 :: c30 -> c35:c36
node :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c36 :: c37 -> c48 -> c48 -> c35:c36
BFTMULT'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c37
enqueue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
ENQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c48
c37 :: c30 -> c57 -> c37
matrixMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
MATRIXMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c57
COMPUTELINE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c38
c38 :: c39:c40 -> c38
COMPUTELINE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c39:c40
c39 :: c41:c42 -> c39:c40
COMPUTELINE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c41:c42
c40 :: c39:c40
c41 :: c38 -> c50 -> c41:c42
lineMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
LINEMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c50
c42 :: c41:c42
c43 :: c44:c45 -> c43
DEQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c44:c45
c44 :: c44:c45
c45 :: c46:c47 -> c61 -> c44:c45
DEQUEUE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c46:c47
reverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
REVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c61
c46 :: c46:c47
c47 :: c46:c47
c48 :: c49 -> c48
ENQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c49
c49 :: c49
c50 :: c51:c52 -> c50
LINEMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c51:c52
c51 :: c53:c54:c55:c56 -> c51:c52
LINEMULT#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c52 :: c51:c52
c53 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c54 :: c50 -> c53:c54:c55:c56
c55 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c56 :: c50 -> c53:c54:c55:c56
c57 :: c58:c59:c60 -> c57
MATRIXMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c58:c59:c60
c58 :: c38 -> c58:c59:c60
c59 :: c57 -> c58:c59:c60
c60 :: c58:c59:c60
c61 :: c26 -> c61
#0 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c :: c:c1:c2:c3:c4
#neg :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#s :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c1 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4
#PRED :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c16:c17:c18:c19
c2 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
#add :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#pos :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c3 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4
#SUCC :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c20:c21:c22:c23
c4 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
c5 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c6 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c7 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c8 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c9 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
#NATMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c14:c15
c10 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c11 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c12 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c13 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c14 :: c14:c15
c15 :: c:c1:c2:c3:c4 -> c14:c15 -> c14:c15
#natmult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c16 :: c16:c17:c18:c19
c17 :: c16:c17:c18:c19
c18 :: c16:c17:c18:c19
c19 :: c16:c17:c18:c19
c20 :: c20:c21:c22:c23
c21 :: c20:c21:c22:c23
c22 :: c20:c21:c22:c23
c23 :: c20:c21:c22:c23
#pred :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#succ :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#mult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
enqueue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
matrixMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos1_62 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c5:c6:c7:c8:c9:c10:c11:c12:c132_62 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
hole_c:c1:c2:c3:c43_62 :: c:c1:c2:c3:c4
hole_c264_62 :: c26
hole_c27:c285_62 :: c27:c28
hole_c296_62 :: c29
hole_c307_62 :: c30
hole_c318_62 :: c31
hole_c329_62 :: c32
hole_c33:c3410_62 :: c33:c34
hole_c4311_62 :: c43
hole_c35:c3612_62 :: c35:c36
hole_c3713_62 :: c37
hole_c4814_62 :: c48
hole_c5715_62 :: c57
hole_c3816_62 :: c38
hole_c39:c4017_62 :: c39:c40
hole_c41:c4218_62 :: c41:c42
hole_c5019_62 :: c50
hole_c44:c4520_62 :: c44:c45
hole_c46:c4721_62 :: c46:c47
hole_c6122_62 :: c61
hole_c4923_62 :: c49
hole_c51:c5224_62 :: c51:c52
hole_c53:c54:c55:c5625_62 :: c53:c54:c55:c56
hole_c58:c59:c6026_62 :: c58:c59:c60
hole_c16:c17:c18:c1927_62 :: c16:c17:c18:c19
hole_c20:c21:c22:c2328_62 :: c20:c21:c22:c23
hole_c14:c1529_62 :: c14:c15
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62 :: Nat -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
gen_c:c1:c2:c3:c431_62 :: Nat -> c:c1:c2:c3:c4
gen_c14:c1532_62 :: Nat -> c14:c15


Lemmas:
appendreverse#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n250_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n250_62, b)), rt in Omega(0)
LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n60901_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n60901_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n60901_62)
LINEMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62)) -> *33_62, rt in Omega(n30296_62)
lineMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n94689_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n94689_62)
lineMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n4908489_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0)) -> *33_62, rt in Omega(n4908489_62)


Generator Equations:
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0) <=> nil
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(x, 1)) <=> ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(x))
gen_c:c1:c2:c3:c431_62(0) <=> c
gen_c:c1:c2:c3:c431_62(+(x, 1)) <=> c2(c16, gen_c:c1:c2:c3:c431_62(x))
gen_c14:c1532_62(0) <=> c14
gen_c14:c1532_62(+(x, 1)) <=> c15(c, gen_c14:c1532_62(x))


The following defined symbols remain to be analysed:
lineMult#1, APPENDREVERSE, APPENDREVERSE#1, BFTMULT', BFTMULT'#1, matrixMult, MATRIXMULT, COMPUTELINE, COMPUTELINE#1, MATRIXMULT#1, bftMult', bftMult'#1, computeLine, computeLine#1, matrixMult#1

They will be analysed ascendingly in the following order:
APPENDREVERSE = APPENDREVERSE#1
BFTMULT' = BFTMULT'#1
matrixMult < BFTMULT'#1
MATRIXMULT < BFTMULT'#1
matrixMult < bftMult'#1
matrixMult = matrixMult#1
MATRIXMULT = MATRIXMULT#1
COMPUTELINE = COMPUTELINE#1
COMPUTELINE < MATRIXMULT#1
lineMult < COMPUTELINE#1
lineMult < computeLine#1
lineMult = lineMult#1
bftMult' = bftMult'#1
computeLine = computeLine#1
computeLine < matrixMult#1

----------------------------------------

(29) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
lineMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n9704981_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n9704981_62)

Induction Base:
lineMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, 0)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c))

Induction Step:
lineMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, +(n9704981_62, 1))), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) ->_R^Omega(0)
lineMult#2(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c), nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n9704981_62))) ->_R^Omega(0)
::(*'(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)), lineMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n9704981_62)), nil)) ->_R^Omega(1)
::(c24(#MULT(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c))), lineMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n9704981_62)), nil)) ->_R^Omega(0)
::(c24(#MULT(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c))), lineMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n9704981_62)), nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c))) ->_IH
::(c24(#MULT(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c))), *33_62)

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(30)
Obligation:
Innermost TRS:
Rules:
*'(z0, z1) -> c24(#MULT(z0, z1))
+'(z0, z1) -> c25(#ADD(z0, z1))
APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
APPENDREVERSE#1(nil, z0) -> c28
BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
BFTMULT'#3(nil, z0, z1) -> c34
BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
COMPUTELINE#1(nil, z0, z1) -> c40
COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
COMPUTELINE#2(nil, z0, z1, z2) -> c42
DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
DEQUEUE#1(::(z0, z1), z2) -> c44
DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
DEQUEUE#2(::(z0, z1)) -> c46
DEQUEUE#2(nil) -> c47
ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
LINEMULT#1(nil, z0, z1) -> c52
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*'(z3, z2), z0), *'(z3, z2))
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
MATRIXMULT#1(nil, z0) -> c60
REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))
#ADD(#0, z0) -> c
#ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
#ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
#ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#MULT(#0, #0) -> c5
#MULT(#0, #neg(z0)) -> c6
#MULT(#0, #pos(z0)) -> c7
#MULT(#neg(z0), #0) -> c8
#MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
#MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
#MULT(#pos(z0), #0) -> c11
#MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
#MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
#NATMULT(#0, z0) -> c14
#NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
#PRED(#0) -> c16
#PRED(#neg(#s(z0))) -> c17
#PRED(#pos(#s(#0))) -> c18
#PRED(#pos(#s(#s(z0)))) -> c19
#SUCC(#0) -> c20
#SUCC(#neg(#s(#0))) -> c21
#SUCC(#neg(#s(#s(z0)))) -> c22
#SUCC(#pos(#s(z0))) -> c23
#add(#0, z0) -> z0
#add(#neg(#s(#0)), z0) -> #pred(z0)
#add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
#add(#pos(#s(#0)), z0) -> #succ(z0)
#add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
#mult(#0, #0) -> #0
#mult(#0, #neg(z0)) -> #0
#mult(#0, #pos(z0)) -> #0
#mult(#neg(z0), #0) -> #0
#mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
#mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #0) -> #0
#mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
#natmult(#0, z0) -> #0
#natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
#pred(#0) -> #neg(#s(#0))
#pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
#pred(#pos(#s(#0))) -> #0
#pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
#succ(#0) -> #pos(#s(#0))
#succ(#neg(#s(#0))) -> #0
#succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
#succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
*'(z0, z1) -> #mult(z0, z1)
+'(z0, z1) -> #add(z0, z1)
appendreverse(z0, z1) -> appendreverse#1(z0, z1)
appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
appendreverse#1(nil, z0) -> z0
bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
bftMult'#3(nil, z0, z1) -> z0
bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
computeLine#1(nil, z0, z1) -> z0
computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
computeLine#2(nil, z0, z1, z2) -> nil
dequeue(z0, z1) -> dequeue#1(z0, z1)
dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
enqueue(z0, z1) -> enqueue#1(z1, z0)
enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
lineMult#1(nil, z0, z1) -> nil
lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+'(*'(z3, z2), z0), lineMult(z2, z4, z1))
lineMult#2(nil, z0, z1, z2) -> ::(*'(z1, z0), lineMult(z0, z2, nil))
matrixMult(z0, z1) -> matrixMult#1(z0, z1)
matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
matrixMult#1(nil, z0) -> nil
reverse(z0) -> appendreverse(z0, nil)

Types:
*' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c24 :: c5:c6:c7:c8:c9:c10:c11:c12:c13 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#MULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c5:c6:c7:c8:c9:c10:c11:c12:c13
+' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c25 :: c:c1:c2:c3:c4 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#ADD :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c:c1:c2:c3:c4
APPENDREVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c26
c26 :: c27:c28 -> c26
APPENDREVERSE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c27:c28
:: :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c27 :: c26 -> c27:c28
nil :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c28 :: c27:c28
BFTMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c29
c29 :: c30 -> c29
BFTMULT' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c30
tuple#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c30 :: c31 -> c32 -> c30
BFTMULT'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c31
bftMult'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
BFTMULT'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c32
c31 :: c33:c34 -> c31
BFTMULT'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c33:c34
c32 :: c43 -> c32
DEQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c43
c33 :: c35:c36 -> c33:c34
BFTMULT'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c35:c36
c34 :: c33:c34
leaf :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c35 :: c30 -> c35:c36
node :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c36 :: c37 -> c48 -> c48 -> c35:c36
BFTMULT'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c37
enqueue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
ENQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c48
c37 :: c30 -> c57 -> c37
matrixMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
MATRIXMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c57
COMPUTELINE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c38
c38 :: c39:c40 -> c38
COMPUTELINE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c39:c40
c39 :: c41:c42 -> c39:c40
COMPUTELINE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c41:c42
c40 :: c39:c40
c41 :: c38 -> c50 -> c41:c42
lineMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
LINEMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c50
c42 :: c41:c42
c43 :: c44:c45 -> c43
DEQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c44:c45
c44 :: c44:c45
c45 :: c46:c47 -> c61 -> c44:c45
DEQUEUE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c46:c47
reverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
REVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c61
c46 :: c46:c47
c47 :: c46:c47
c48 :: c49 -> c48
ENQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c49
c49 :: c49
c50 :: c51:c52 -> c50
LINEMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c51:c52
c51 :: c53:c54:c55:c56 -> c51:c52
LINEMULT#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c52 :: c51:c52
c53 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c54 :: c50 -> c53:c54:c55:c56
c55 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c56 :: c50 -> c53:c54:c55:c56
c57 :: c58:c59:c60 -> c57
MATRIXMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c58:c59:c60
c58 :: c38 -> c58:c59:c60
c59 :: c57 -> c58:c59:c60
c60 :: c58:c59:c60
c61 :: c26 -> c61
#0 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c :: c:c1:c2:c3:c4
#neg :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#s :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c1 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4
#PRED :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c16:c17:c18:c19
c2 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
#add :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#pos :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c3 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4
#SUCC :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c20:c21:c22:c23
c4 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
c5 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c6 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c7 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c8 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c9 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
#NATMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c14:c15
c10 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c11 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c12 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c13 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c14 :: c14:c15
c15 :: c:c1:c2:c3:c4 -> c14:c15 -> c14:c15
#natmult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c16 :: c16:c17:c18:c19
c17 :: c16:c17:c18:c19
c18 :: c16:c17:c18:c19
c19 :: c16:c17:c18:c19
c20 :: c20:c21:c22:c23
c21 :: c20:c21:c22:c23
c22 :: c20:c21:c22:c23
c23 :: c20:c21:c22:c23
#pred :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#succ :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#mult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
enqueue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
matrixMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos1_62 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c5:c6:c7:c8:c9:c10:c11:c12:c132_62 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
hole_c:c1:c2:c3:c43_62 :: c:c1:c2:c3:c4
hole_c264_62 :: c26
hole_c27:c285_62 :: c27:c28
hole_c296_62 :: c29
hole_c307_62 :: c30
hole_c318_62 :: c31
hole_c329_62 :: c32
hole_c33:c3410_62 :: c33:c34
hole_c4311_62 :: c43
hole_c35:c3612_62 :: c35:c36
hole_c3713_62 :: c37
hole_c4814_62 :: c48
hole_c5715_62 :: c57
hole_c3816_62 :: c38
hole_c39:c4017_62 :: c39:c40
hole_c41:c4218_62 :: c41:c42
hole_c5019_62 :: c50
hole_c44:c4520_62 :: c44:c45
hole_c46:c4721_62 :: c46:c47
hole_c6122_62 :: c61
hole_c4923_62 :: c49
hole_c51:c5224_62 :: c51:c52
hole_c53:c54:c55:c5625_62 :: c53:c54:c55:c56
hole_c58:c59:c6026_62 :: c58:c59:c60
hole_c16:c17:c18:c1927_62 :: c16:c17:c18:c19
hole_c20:c21:c22:c2328_62 :: c20:c21:c22:c23
hole_c14:c1529_62 :: c14:c15
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62 :: Nat -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
gen_c:c1:c2:c3:c431_62 :: Nat -> c:c1:c2:c3:c4
gen_c14:c1532_62 :: Nat -> c14:c15


Lemmas:
appendreverse#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n250_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n250_62, b)), rt in Omega(0)
LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n60901_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n60901_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n60901_62)
LINEMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62)) -> *33_62, rt in Omega(n30296_62)
lineMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n9704981_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n9704981_62)
lineMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n4908489_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0)) -> *33_62, rt in Omega(n4908489_62)


Generator Equations:
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0) <=> nil
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(x, 1)) <=> ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(x))
gen_c:c1:c2:c3:c431_62(0) <=> c
gen_c:c1:c2:c3:c431_62(+(x, 1)) <=> c2(c16, gen_c:c1:c2:c3:c431_62(x))
gen_c14:c1532_62(0) <=> c14
gen_c14:c1532_62(+(x, 1)) <=> c15(c, gen_c14:c1532_62(x))


The following defined symbols remain to be analysed:
computeLine#1, APPENDREVERSE, APPENDREVERSE#1, BFTMULT', BFTMULT'#1, matrixMult, MATRIXMULT, COMPUTELINE, COMPUTELINE#1, MATRIXMULT#1, bftMult', bftMult'#1, computeLine, matrixMult#1

They will be analysed ascendingly in the following order:
APPENDREVERSE = APPENDREVERSE#1
BFTMULT' = BFTMULT'#1
matrixMult < BFTMULT'#1
MATRIXMULT < BFTMULT'#1
matrixMult < bftMult'#1
matrixMult = matrixMult#1
MATRIXMULT = MATRIXMULT#1
COMPUTELINE = COMPUTELINE#1
COMPUTELINE < MATRIXMULT#1
bftMult' = bftMult'#1
computeLine = computeLine#1
computeLine < matrixMult#1

----------------------------------------

(31) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
MATRIXMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14767818_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14767818_62)

Induction Base:
MATRIXMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, 0)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))

Induction Step:
MATRIXMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, +(n14767818_62, 1))), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) ->_R^Omega(1)
c59(MATRIXMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14767818_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))) ->_R^Omega(1)
c59(c57(MATRIXMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14767818_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)))) ->_IH
c59(c57(*33_62))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(32)
Obligation:
Innermost TRS:
Rules:
*'(z0, z1) -> c24(#MULT(z0, z1))
+'(z0, z1) -> c25(#ADD(z0, z1))
APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
APPENDREVERSE#1(nil, z0) -> c28
BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
BFTMULT'#3(nil, z0, z1) -> c34
BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
COMPUTELINE#1(nil, z0, z1) -> c40
COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
COMPUTELINE#2(nil, z0, z1, z2) -> c42
DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
DEQUEUE#1(::(z0, z1), z2) -> c44
DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
DEQUEUE#2(::(z0, z1)) -> c46
DEQUEUE#2(nil) -> c47
ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
LINEMULT#1(nil, z0, z1) -> c52
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*'(z3, z2), z0), *'(z3, z2))
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
MATRIXMULT#1(nil, z0) -> c60
REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))
#ADD(#0, z0) -> c
#ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
#ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
#ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#MULT(#0, #0) -> c5
#MULT(#0, #neg(z0)) -> c6
#MULT(#0, #pos(z0)) -> c7
#MULT(#neg(z0), #0) -> c8
#MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
#MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
#MULT(#pos(z0), #0) -> c11
#MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
#MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
#NATMULT(#0, z0) -> c14
#NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
#PRED(#0) -> c16
#PRED(#neg(#s(z0))) -> c17
#PRED(#pos(#s(#0))) -> c18
#PRED(#pos(#s(#s(z0)))) -> c19
#SUCC(#0) -> c20
#SUCC(#neg(#s(#0))) -> c21
#SUCC(#neg(#s(#s(z0)))) -> c22
#SUCC(#pos(#s(z0))) -> c23
#add(#0, z0) -> z0
#add(#neg(#s(#0)), z0) -> #pred(z0)
#add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
#add(#pos(#s(#0)), z0) -> #succ(z0)
#add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
#mult(#0, #0) -> #0
#mult(#0, #neg(z0)) -> #0
#mult(#0, #pos(z0)) -> #0
#mult(#neg(z0), #0) -> #0
#mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
#mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #0) -> #0
#mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
#natmult(#0, z0) -> #0
#natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
#pred(#0) -> #neg(#s(#0))
#pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
#pred(#pos(#s(#0))) -> #0
#pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
#succ(#0) -> #pos(#s(#0))
#succ(#neg(#s(#0))) -> #0
#succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
#succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
*'(z0, z1) -> #mult(z0, z1)
+'(z0, z1) -> #add(z0, z1)
appendreverse(z0, z1) -> appendreverse#1(z0, z1)
appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
appendreverse#1(nil, z0) -> z0
bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
bftMult'#3(nil, z0, z1) -> z0
bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
computeLine#1(nil, z0, z1) -> z0
computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
computeLine#2(nil, z0, z1, z2) -> nil
dequeue(z0, z1) -> dequeue#1(z0, z1)
dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
enqueue(z0, z1) -> enqueue#1(z1, z0)
enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
lineMult#1(nil, z0, z1) -> nil
lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+'(*'(z3, z2), z0), lineMult(z2, z4, z1))
lineMult#2(nil, z0, z1, z2) -> ::(*'(z1, z0), lineMult(z0, z2, nil))
matrixMult(z0, z1) -> matrixMult#1(z0, z1)
matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
matrixMult#1(nil, z0) -> nil
reverse(z0) -> appendreverse(z0, nil)

Types:
*' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c24 :: c5:c6:c7:c8:c9:c10:c11:c12:c13 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#MULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c5:c6:c7:c8:c9:c10:c11:c12:c13
+' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c25 :: c:c1:c2:c3:c4 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#ADD :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c:c1:c2:c3:c4
APPENDREVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c26
c26 :: c27:c28 -> c26
APPENDREVERSE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c27:c28
:: :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c27 :: c26 -> c27:c28
nil :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c28 :: c27:c28
BFTMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c29
c29 :: c30 -> c29
BFTMULT' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c30
tuple#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c30 :: c31 -> c32 -> c30
BFTMULT'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c31
bftMult'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
BFTMULT'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c32
c31 :: c33:c34 -> c31
BFTMULT'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c33:c34
c32 :: c43 -> c32
DEQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c43
c33 :: c35:c36 -> c33:c34
BFTMULT'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c35:c36
c34 :: c33:c34
leaf :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c35 :: c30 -> c35:c36
node :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c36 :: c37 -> c48 -> c48 -> c35:c36
BFTMULT'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c37
enqueue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
ENQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c48
c37 :: c30 -> c57 -> c37
matrixMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
MATRIXMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c57
COMPUTELINE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c38
c38 :: c39:c40 -> c38
COMPUTELINE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c39:c40
c39 :: c41:c42 -> c39:c40
COMPUTELINE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c41:c42
c40 :: c39:c40
c41 :: c38 -> c50 -> c41:c42
lineMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
LINEMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c50
c42 :: c41:c42
c43 :: c44:c45 -> c43
DEQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c44:c45
c44 :: c44:c45
c45 :: c46:c47 -> c61 -> c44:c45
DEQUEUE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c46:c47
reverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
REVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c61
c46 :: c46:c47
c47 :: c46:c47
c48 :: c49 -> c48
ENQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c49
c49 :: c49
c50 :: c51:c52 -> c50
LINEMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c51:c52
c51 :: c53:c54:c55:c56 -> c51:c52
LINEMULT#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c52 :: c51:c52
c53 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c54 :: c50 -> c53:c54:c55:c56
c55 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c56 :: c50 -> c53:c54:c55:c56
c57 :: c58:c59:c60 -> c57
MATRIXMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c58:c59:c60
c58 :: c38 -> c58:c59:c60
c59 :: c57 -> c58:c59:c60
c60 :: c58:c59:c60
c61 :: c26 -> c61
#0 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c :: c:c1:c2:c3:c4
#neg :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#s :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c1 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4
#PRED :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c16:c17:c18:c19
c2 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
#add :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#pos :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c3 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4
#SUCC :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c20:c21:c22:c23
c4 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
c5 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c6 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c7 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c8 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c9 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
#NATMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c14:c15
c10 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c11 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c12 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c13 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c14 :: c14:c15
c15 :: c:c1:c2:c3:c4 -> c14:c15 -> c14:c15
#natmult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c16 :: c16:c17:c18:c19
c17 :: c16:c17:c18:c19
c18 :: c16:c17:c18:c19
c19 :: c16:c17:c18:c19
c20 :: c20:c21:c22:c23
c21 :: c20:c21:c22:c23
c22 :: c20:c21:c22:c23
c23 :: c20:c21:c22:c23
#pred :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#succ :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#mult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
enqueue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
matrixMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos1_62 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c5:c6:c7:c8:c9:c10:c11:c12:c132_62 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
hole_c:c1:c2:c3:c43_62 :: c:c1:c2:c3:c4
hole_c264_62 :: c26
hole_c27:c285_62 :: c27:c28
hole_c296_62 :: c29
hole_c307_62 :: c30
hole_c318_62 :: c31
hole_c329_62 :: c32
hole_c33:c3410_62 :: c33:c34
hole_c4311_62 :: c43
hole_c35:c3612_62 :: c35:c36
hole_c3713_62 :: c37
hole_c4814_62 :: c48
hole_c5715_62 :: c57
hole_c3816_62 :: c38
hole_c39:c4017_62 :: c39:c40
hole_c41:c4218_62 :: c41:c42
hole_c5019_62 :: c50
hole_c44:c4520_62 :: c44:c45
hole_c46:c4721_62 :: c46:c47
hole_c6122_62 :: c61
hole_c4923_62 :: c49
hole_c51:c5224_62 :: c51:c52
hole_c53:c54:c55:c5625_62 :: c53:c54:c55:c56
hole_c58:c59:c6026_62 :: c58:c59:c60
hole_c16:c17:c18:c1927_62 :: c16:c17:c18:c19
hole_c20:c21:c22:c2328_62 :: c20:c21:c22:c23
hole_c14:c1529_62 :: c14:c15
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62 :: Nat -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
gen_c:c1:c2:c3:c431_62 :: Nat -> c:c1:c2:c3:c4
gen_c14:c1532_62 :: Nat -> c14:c15


Lemmas:
appendreverse#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n250_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n250_62, b)), rt in Omega(0)
LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n60901_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n60901_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n60901_62)
LINEMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62)) -> *33_62, rt in Omega(n30296_62)
lineMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n9704981_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n9704981_62)
lineMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n4908489_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0)) -> *33_62, rt in Omega(n4908489_62)
MATRIXMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14767818_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14767818_62)


Generator Equations:
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0) <=> nil
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(x, 1)) <=> ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(x))
gen_c:c1:c2:c3:c431_62(0) <=> c
gen_c:c1:c2:c3:c431_62(+(x, 1)) <=> c2(c16, gen_c:c1:c2:c3:c431_62(x))
gen_c14:c1532_62(0) <=> c14
gen_c14:c1532_62(+(x, 1)) <=> c15(c, gen_c14:c1532_62(x))


The following defined symbols remain to be analysed:
MATRIXMULT, APPENDREVERSE, APPENDREVERSE#1, BFTMULT', BFTMULT'#1, matrixMult, bftMult', bftMult'#1, matrixMult#1

They will be analysed ascendingly in the following order:
APPENDREVERSE = APPENDREVERSE#1
BFTMULT' = BFTMULT'#1
matrixMult < BFTMULT'#1
MATRIXMULT < BFTMULT'#1
matrixMult < bftMult'#1
matrixMult = matrixMult#1
MATRIXMULT = MATRIXMULT#1
bftMult' = bftMult'#1

----------------------------------------

(33) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
MATRIXMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14779477_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14779477_62)

Induction Base:
MATRIXMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))

Induction Step:
MATRIXMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n14779477_62, 1)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) ->_R^Omega(1)
c57(MATRIXMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n14779477_62, 1)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))) ->_R^Omega(1)
c57(c59(MATRIXMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14779477_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)))) ->_IH
c57(c59(*33_62))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(34)
Obligation:
Innermost TRS:
Rules:
*'(z0, z1) -> c24(#MULT(z0, z1))
+'(z0, z1) -> c25(#ADD(z0, z1))
APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
APPENDREVERSE#1(nil, z0) -> c28
BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
BFTMULT'#3(nil, z0, z1) -> c34
BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
COMPUTELINE#1(nil, z0, z1) -> c40
COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
COMPUTELINE#2(nil, z0, z1, z2) -> c42
DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
DEQUEUE#1(::(z0, z1), z2) -> c44
DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
DEQUEUE#2(::(z0, z1)) -> c46
DEQUEUE#2(nil) -> c47
ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
LINEMULT#1(nil, z0, z1) -> c52
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*'(z3, z2), z0), *'(z3, z2))
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
MATRIXMULT#1(nil, z0) -> c60
REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))
#ADD(#0, z0) -> c
#ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
#ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
#ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#MULT(#0, #0) -> c5
#MULT(#0, #neg(z0)) -> c6
#MULT(#0, #pos(z0)) -> c7
#MULT(#neg(z0), #0) -> c8
#MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
#MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
#MULT(#pos(z0), #0) -> c11
#MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
#MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
#NATMULT(#0, z0) -> c14
#NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
#PRED(#0) -> c16
#PRED(#neg(#s(z0))) -> c17
#PRED(#pos(#s(#0))) -> c18
#PRED(#pos(#s(#s(z0)))) -> c19
#SUCC(#0) -> c20
#SUCC(#neg(#s(#0))) -> c21
#SUCC(#neg(#s(#s(z0)))) -> c22
#SUCC(#pos(#s(z0))) -> c23
#add(#0, z0) -> z0
#add(#neg(#s(#0)), z0) -> #pred(z0)
#add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
#add(#pos(#s(#0)), z0) -> #succ(z0)
#add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
#mult(#0, #0) -> #0
#mult(#0, #neg(z0)) -> #0
#mult(#0, #pos(z0)) -> #0
#mult(#neg(z0), #0) -> #0
#mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
#mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #0) -> #0
#mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
#natmult(#0, z0) -> #0
#natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
#pred(#0) -> #neg(#s(#0))
#pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
#pred(#pos(#s(#0))) -> #0
#pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
#succ(#0) -> #pos(#s(#0))
#succ(#neg(#s(#0))) -> #0
#succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
#succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
*'(z0, z1) -> #mult(z0, z1)
+'(z0, z1) -> #add(z0, z1)
appendreverse(z0, z1) -> appendreverse#1(z0, z1)
appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
appendreverse#1(nil, z0) -> z0
bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
bftMult'#3(nil, z0, z1) -> z0
bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
computeLine#1(nil, z0, z1) -> z0
computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
computeLine#2(nil, z0, z1, z2) -> nil
dequeue(z0, z1) -> dequeue#1(z0, z1)
dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
enqueue(z0, z1) -> enqueue#1(z1, z0)
enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
lineMult#1(nil, z0, z1) -> nil
lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+'(*'(z3, z2), z0), lineMult(z2, z4, z1))
lineMult#2(nil, z0, z1, z2) -> ::(*'(z1, z0), lineMult(z0, z2, nil))
matrixMult(z0, z1) -> matrixMult#1(z0, z1)
matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
matrixMult#1(nil, z0) -> nil
reverse(z0) -> appendreverse(z0, nil)

Types:
*' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c24 :: c5:c6:c7:c8:c9:c10:c11:c12:c13 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#MULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c5:c6:c7:c8:c9:c10:c11:c12:c13
+' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c25 :: c:c1:c2:c3:c4 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#ADD :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c:c1:c2:c3:c4
APPENDREVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c26
c26 :: c27:c28 -> c26
APPENDREVERSE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c27:c28
:: :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c27 :: c26 -> c27:c28
nil :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c28 :: c27:c28
BFTMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c29
c29 :: c30 -> c29
BFTMULT' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c30
tuple#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c30 :: c31 -> c32 -> c30
BFTMULT'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c31
bftMult'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
BFTMULT'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c32
c31 :: c33:c34 -> c31
BFTMULT'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c33:c34
c32 :: c43 -> c32
DEQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c43
c33 :: c35:c36 -> c33:c34
BFTMULT'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c35:c36
c34 :: c33:c34
leaf :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c35 :: c30 -> c35:c36
node :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c36 :: c37 -> c48 -> c48 -> c35:c36
BFTMULT'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c37
enqueue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
ENQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c48
c37 :: c30 -> c57 -> c37
matrixMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
MATRIXMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c57
COMPUTELINE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c38
c38 :: c39:c40 -> c38
COMPUTELINE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c39:c40
c39 :: c41:c42 -> c39:c40
COMPUTELINE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c41:c42
c40 :: c39:c40
c41 :: c38 -> c50 -> c41:c42
lineMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
LINEMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c50
c42 :: c41:c42
c43 :: c44:c45 -> c43
DEQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c44:c45
c44 :: c44:c45
c45 :: c46:c47 -> c61 -> c44:c45
DEQUEUE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c46:c47
reverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
REVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c61
c46 :: c46:c47
c47 :: c46:c47
c48 :: c49 -> c48
ENQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c49
c49 :: c49
c50 :: c51:c52 -> c50
LINEMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c51:c52
c51 :: c53:c54:c55:c56 -> c51:c52
LINEMULT#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c52 :: c51:c52
c53 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c54 :: c50 -> c53:c54:c55:c56
c55 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c56 :: c50 -> c53:c54:c55:c56
c57 :: c58:c59:c60 -> c57
MATRIXMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c58:c59:c60
c58 :: c38 -> c58:c59:c60
c59 :: c57 -> c58:c59:c60
c60 :: c58:c59:c60
c61 :: c26 -> c61
#0 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c :: c:c1:c2:c3:c4
#neg :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#s :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c1 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4
#PRED :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c16:c17:c18:c19
c2 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
#add :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#pos :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c3 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4
#SUCC :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c20:c21:c22:c23
c4 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
c5 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c6 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c7 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c8 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c9 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
#NATMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c14:c15
c10 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c11 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c12 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c13 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c14 :: c14:c15
c15 :: c:c1:c2:c3:c4 -> c14:c15 -> c14:c15
#natmult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c16 :: c16:c17:c18:c19
c17 :: c16:c17:c18:c19
c18 :: c16:c17:c18:c19
c19 :: c16:c17:c18:c19
c20 :: c20:c21:c22:c23
c21 :: c20:c21:c22:c23
c22 :: c20:c21:c22:c23
c23 :: c20:c21:c22:c23
#pred :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#succ :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#mult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
enqueue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
matrixMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos1_62 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c5:c6:c7:c8:c9:c10:c11:c12:c132_62 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
hole_c:c1:c2:c3:c43_62 :: c:c1:c2:c3:c4
hole_c264_62 :: c26
hole_c27:c285_62 :: c27:c28
hole_c296_62 :: c29
hole_c307_62 :: c30
hole_c318_62 :: c31
hole_c329_62 :: c32
hole_c33:c3410_62 :: c33:c34
hole_c4311_62 :: c43
hole_c35:c3612_62 :: c35:c36
hole_c3713_62 :: c37
hole_c4814_62 :: c48
hole_c5715_62 :: c57
hole_c3816_62 :: c38
hole_c39:c4017_62 :: c39:c40
hole_c41:c4218_62 :: c41:c42
hole_c5019_62 :: c50
hole_c44:c4520_62 :: c44:c45
hole_c46:c4721_62 :: c46:c47
hole_c6122_62 :: c61
hole_c4923_62 :: c49
hole_c51:c5224_62 :: c51:c52
hole_c53:c54:c55:c5625_62 :: c53:c54:c55:c56
hole_c58:c59:c6026_62 :: c58:c59:c60
hole_c16:c17:c18:c1927_62 :: c16:c17:c18:c19
hole_c20:c21:c22:c2328_62 :: c20:c21:c22:c23
hole_c14:c1529_62 :: c14:c15
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62 :: Nat -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
gen_c:c1:c2:c3:c431_62 :: Nat -> c:c1:c2:c3:c4
gen_c14:c1532_62 :: Nat -> c14:c15


Lemmas:
appendreverse#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n250_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n250_62, b)), rt in Omega(0)
LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n60901_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n60901_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n60901_62)
LINEMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62)) -> *33_62, rt in Omega(n30296_62)
lineMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n9704981_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n9704981_62)
lineMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n4908489_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0)) -> *33_62, rt in Omega(n4908489_62)
MATRIXMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14767818_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14767818_62)
MATRIXMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14779477_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14779477_62)


Generator Equations:
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0) <=> nil
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(x, 1)) <=> ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(x))
gen_c:c1:c2:c3:c431_62(0) <=> c
gen_c:c1:c2:c3:c431_62(+(x, 1)) <=> c2(c16, gen_c:c1:c2:c3:c431_62(x))
gen_c14:c1532_62(0) <=> c14
gen_c14:c1532_62(+(x, 1)) <=> c15(c, gen_c14:c1532_62(x))


The following defined symbols remain to be analysed:
MATRIXMULT#1, APPENDREVERSE, APPENDREVERSE#1, BFTMULT', BFTMULT'#1, matrixMult, bftMult', bftMult'#1, matrixMult#1

They will be analysed ascendingly in the following order:
APPENDREVERSE = APPENDREVERSE#1
BFTMULT' = BFTMULT'#1
matrixMult < BFTMULT'#1
MATRIXMULT < BFTMULT'#1
matrixMult < bftMult'#1
matrixMult = matrixMult#1
MATRIXMULT = MATRIXMULT#1
bftMult' = bftMult'#1

----------------------------------------

(35) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
MATRIXMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14791201_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14791201_62)

Induction Base:
MATRIXMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, 0)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))

Induction Step:
MATRIXMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, +(n14791201_62, 1))), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) ->_R^Omega(1)
c59(MATRIXMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14791201_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))) ->_R^Omega(1)
c59(c57(MATRIXMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14791201_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)))) ->_IH
c59(c57(*33_62))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(36)
Obligation:
Innermost TRS:
Rules:
*'(z0, z1) -> c24(#MULT(z0, z1))
+'(z0, z1) -> c25(#ADD(z0, z1))
APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
APPENDREVERSE#1(nil, z0) -> c28
BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
BFTMULT'#3(nil, z0, z1) -> c34
BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
COMPUTELINE#1(nil, z0, z1) -> c40
COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
COMPUTELINE#2(nil, z0, z1, z2) -> c42
DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
DEQUEUE#1(::(z0, z1), z2) -> c44
DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
DEQUEUE#2(::(z0, z1)) -> c46
DEQUEUE#2(nil) -> c47
ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
LINEMULT#1(nil, z0, z1) -> c52
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*'(z3, z2), z0), *'(z3, z2))
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
MATRIXMULT#1(nil, z0) -> c60
REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))
#ADD(#0, z0) -> c
#ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
#ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
#ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#MULT(#0, #0) -> c5
#MULT(#0, #neg(z0)) -> c6
#MULT(#0, #pos(z0)) -> c7
#MULT(#neg(z0), #0) -> c8
#MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
#MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
#MULT(#pos(z0), #0) -> c11
#MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
#MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
#NATMULT(#0, z0) -> c14
#NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
#PRED(#0) -> c16
#PRED(#neg(#s(z0))) -> c17
#PRED(#pos(#s(#0))) -> c18
#PRED(#pos(#s(#s(z0)))) -> c19
#SUCC(#0) -> c20
#SUCC(#neg(#s(#0))) -> c21
#SUCC(#neg(#s(#s(z0)))) -> c22
#SUCC(#pos(#s(z0))) -> c23
#add(#0, z0) -> z0
#add(#neg(#s(#0)), z0) -> #pred(z0)
#add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
#add(#pos(#s(#0)), z0) -> #succ(z0)
#add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
#mult(#0, #0) -> #0
#mult(#0, #neg(z0)) -> #0
#mult(#0, #pos(z0)) -> #0
#mult(#neg(z0), #0) -> #0
#mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
#mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #0) -> #0
#mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
#natmult(#0, z0) -> #0
#natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
#pred(#0) -> #neg(#s(#0))
#pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
#pred(#pos(#s(#0))) -> #0
#pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
#succ(#0) -> #pos(#s(#0))
#succ(#neg(#s(#0))) -> #0
#succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
#succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
*'(z0, z1) -> #mult(z0, z1)
+'(z0, z1) -> #add(z0, z1)
appendreverse(z0, z1) -> appendreverse#1(z0, z1)
appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
appendreverse#1(nil, z0) -> z0
bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
bftMult'#3(nil, z0, z1) -> z0
bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
computeLine#1(nil, z0, z1) -> z0
computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
computeLine#2(nil, z0, z1, z2) -> nil
dequeue(z0, z1) -> dequeue#1(z0, z1)
dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
enqueue(z0, z1) -> enqueue#1(z1, z0)
enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
lineMult#1(nil, z0, z1) -> nil
lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+'(*'(z3, z2), z0), lineMult(z2, z4, z1))
lineMult#2(nil, z0, z1, z2) -> ::(*'(z1, z0), lineMult(z0, z2, nil))
matrixMult(z0, z1) -> matrixMult#1(z0, z1)
matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
matrixMult#1(nil, z0) -> nil
reverse(z0) -> appendreverse(z0, nil)

Types:
*' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c24 :: c5:c6:c7:c8:c9:c10:c11:c12:c13 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#MULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c5:c6:c7:c8:c9:c10:c11:c12:c13
+' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c25 :: c:c1:c2:c3:c4 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#ADD :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c:c1:c2:c3:c4
APPENDREVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c26
c26 :: c27:c28 -> c26
APPENDREVERSE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c27:c28
:: :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c27 :: c26 -> c27:c28
nil :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c28 :: c27:c28
BFTMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c29
c29 :: c30 -> c29
BFTMULT' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c30
tuple#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c30 :: c31 -> c32 -> c30
BFTMULT'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c31
bftMult'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
BFTMULT'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c32
c31 :: c33:c34 -> c31
BFTMULT'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c33:c34
c32 :: c43 -> c32
DEQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c43
c33 :: c35:c36 -> c33:c34
BFTMULT'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c35:c36
c34 :: c33:c34
leaf :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c35 :: c30 -> c35:c36
node :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c36 :: c37 -> c48 -> c48 -> c35:c36
BFTMULT'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c37
enqueue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
ENQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c48
c37 :: c30 -> c57 -> c37
matrixMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
MATRIXMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c57
COMPUTELINE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c38
c38 :: c39:c40 -> c38
COMPUTELINE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c39:c40
c39 :: c41:c42 -> c39:c40
COMPUTELINE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c41:c42
c40 :: c39:c40
c41 :: c38 -> c50 -> c41:c42
lineMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
LINEMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c50
c42 :: c41:c42
c43 :: c44:c45 -> c43
DEQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c44:c45
c44 :: c44:c45
c45 :: c46:c47 -> c61 -> c44:c45
DEQUEUE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c46:c47
reverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
REVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c61
c46 :: c46:c47
c47 :: c46:c47
c48 :: c49 -> c48
ENQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c49
c49 :: c49
c50 :: c51:c52 -> c50
LINEMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c51:c52
c51 :: c53:c54:c55:c56 -> c51:c52
LINEMULT#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c52 :: c51:c52
c53 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c54 :: c50 -> c53:c54:c55:c56
c55 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c56 :: c50 -> c53:c54:c55:c56
c57 :: c58:c59:c60 -> c57
MATRIXMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c58:c59:c60
c58 :: c38 -> c58:c59:c60
c59 :: c57 -> c58:c59:c60
c60 :: c58:c59:c60
c61 :: c26 -> c61
#0 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c :: c:c1:c2:c3:c4
#neg :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#s :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c1 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4
#PRED :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c16:c17:c18:c19
c2 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
#add :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#pos :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c3 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4
#SUCC :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c20:c21:c22:c23
c4 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
c5 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c6 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c7 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c8 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c9 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
#NATMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c14:c15
c10 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c11 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c12 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c13 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c14 :: c14:c15
c15 :: c:c1:c2:c3:c4 -> c14:c15 -> c14:c15
#natmult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c16 :: c16:c17:c18:c19
c17 :: c16:c17:c18:c19
c18 :: c16:c17:c18:c19
c19 :: c16:c17:c18:c19
c20 :: c20:c21:c22:c23
c21 :: c20:c21:c22:c23
c22 :: c20:c21:c22:c23
c23 :: c20:c21:c22:c23
#pred :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#succ :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#mult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
enqueue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
matrixMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos1_62 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c5:c6:c7:c8:c9:c10:c11:c12:c132_62 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
hole_c:c1:c2:c3:c43_62 :: c:c1:c2:c3:c4
hole_c264_62 :: c26
hole_c27:c285_62 :: c27:c28
hole_c296_62 :: c29
hole_c307_62 :: c30
hole_c318_62 :: c31
hole_c329_62 :: c32
hole_c33:c3410_62 :: c33:c34
hole_c4311_62 :: c43
hole_c35:c3612_62 :: c35:c36
hole_c3713_62 :: c37
hole_c4814_62 :: c48
hole_c5715_62 :: c57
hole_c3816_62 :: c38
hole_c39:c4017_62 :: c39:c40
hole_c41:c4218_62 :: c41:c42
hole_c5019_62 :: c50
hole_c44:c4520_62 :: c44:c45
hole_c46:c4721_62 :: c46:c47
hole_c6122_62 :: c61
hole_c4923_62 :: c49
hole_c51:c5224_62 :: c51:c52
hole_c53:c54:c55:c5625_62 :: c53:c54:c55:c56
hole_c58:c59:c6026_62 :: c58:c59:c60
hole_c16:c17:c18:c1927_62 :: c16:c17:c18:c19
hole_c20:c21:c22:c2328_62 :: c20:c21:c22:c23
hole_c14:c1529_62 :: c14:c15
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62 :: Nat -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
gen_c:c1:c2:c3:c431_62 :: Nat -> c:c1:c2:c3:c4
gen_c14:c1532_62 :: Nat -> c14:c15


Lemmas:
appendreverse#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n250_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n250_62, b)), rt in Omega(0)
LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n60901_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n60901_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n60901_62)
LINEMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62)) -> *33_62, rt in Omega(n30296_62)
lineMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n9704981_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n9704981_62)
lineMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n4908489_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0)) -> *33_62, rt in Omega(n4908489_62)
MATRIXMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14791201_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14791201_62)
MATRIXMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14779477_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14779477_62)


Generator Equations:
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0) <=> nil
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(x, 1)) <=> ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(x))
gen_c:c1:c2:c3:c431_62(0) <=> c
gen_c:c1:c2:c3:c431_62(+(x, 1)) <=> c2(c16, gen_c:c1:c2:c3:c431_62(x))
gen_c14:c1532_62(0) <=> c14
gen_c14:c1532_62(+(x, 1)) <=> c15(c, gen_c14:c1532_62(x))


The following defined symbols remain to be analysed:
matrixMult#1, APPENDREVERSE, APPENDREVERSE#1, BFTMULT', BFTMULT'#1, matrixMult, bftMult', bftMult'#1

They will be analysed ascendingly in the following order:
APPENDREVERSE = APPENDREVERSE#1
BFTMULT' = BFTMULT'#1
matrixMult < BFTMULT'#1
matrixMult < bftMult'#1
matrixMult = matrixMult#1
bftMult' = bftMult'#1

----------------------------------------

(37) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
matrixMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14805808_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14805808_62), rt in Omega(0)

Induction Base:
matrixMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) ->_R^Omega(0)
nil

Induction Step:
matrixMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n14805808_62, 1)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) ->_R^Omega(0)
::(computeLine(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b), nil), matrixMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14805808_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))) ->_R^Omega(0)
::(computeLine#1(nil, nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)), matrixMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14805808_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))) ->_R^Omega(0)
::(nil, matrixMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14805808_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))) ->_R^Omega(0)
::(nil, matrixMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14805808_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))) ->_IH
::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c14805809_62))

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(38)
Obligation:
Innermost TRS:
Rules:
*'(z0, z1) -> c24(#MULT(z0, z1))
+'(z0, z1) -> c25(#ADD(z0, z1))
APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
APPENDREVERSE#1(nil, z0) -> c28
BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
BFTMULT'#3(nil, z0, z1) -> c34
BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
COMPUTELINE#1(nil, z0, z1) -> c40
COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
COMPUTELINE#2(nil, z0, z1, z2) -> c42
DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
DEQUEUE#1(::(z0, z1), z2) -> c44
DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
DEQUEUE#2(::(z0, z1)) -> c46
DEQUEUE#2(nil) -> c47
ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
LINEMULT#1(nil, z0, z1) -> c52
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*'(z3, z2), z0), *'(z3, z2))
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
MATRIXMULT#1(nil, z0) -> c60
REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))
#ADD(#0, z0) -> c
#ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
#ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
#ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#MULT(#0, #0) -> c5
#MULT(#0, #neg(z0)) -> c6
#MULT(#0, #pos(z0)) -> c7
#MULT(#neg(z0), #0) -> c8
#MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
#MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
#MULT(#pos(z0), #0) -> c11
#MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
#MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
#NATMULT(#0, z0) -> c14
#NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
#PRED(#0) -> c16
#PRED(#neg(#s(z0))) -> c17
#PRED(#pos(#s(#0))) -> c18
#PRED(#pos(#s(#s(z0)))) -> c19
#SUCC(#0) -> c20
#SUCC(#neg(#s(#0))) -> c21
#SUCC(#neg(#s(#s(z0)))) -> c22
#SUCC(#pos(#s(z0))) -> c23
#add(#0, z0) -> z0
#add(#neg(#s(#0)), z0) -> #pred(z0)
#add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
#add(#pos(#s(#0)), z0) -> #succ(z0)
#add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
#mult(#0, #0) -> #0
#mult(#0, #neg(z0)) -> #0
#mult(#0, #pos(z0)) -> #0
#mult(#neg(z0), #0) -> #0
#mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
#mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #0) -> #0
#mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
#natmult(#0, z0) -> #0
#natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
#pred(#0) -> #neg(#s(#0))
#pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
#pred(#pos(#s(#0))) -> #0
#pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
#succ(#0) -> #pos(#s(#0))
#succ(#neg(#s(#0))) -> #0
#succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
#succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
*'(z0, z1) -> #mult(z0, z1)
+'(z0, z1) -> #add(z0, z1)
appendreverse(z0, z1) -> appendreverse#1(z0, z1)
appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
appendreverse#1(nil, z0) -> z0
bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
bftMult'#3(nil, z0, z1) -> z0
bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
computeLine#1(nil, z0, z1) -> z0
computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
computeLine#2(nil, z0, z1, z2) -> nil
dequeue(z0, z1) -> dequeue#1(z0, z1)
dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
enqueue(z0, z1) -> enqueue#1(z1, z0)
enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
lineMult#1(nil, z0, z1) -> nil
lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+'(*'(z3, z2), z0), lineMult(z2, z4, z1))
lineMult#2(nil, z0, z1, z2) -> ::(*'(z1, z0), lineMult(z0, z2, nil))
matrixMult(z0, z1) -> matrixMult#1(z0, z1)
matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
matrixMult#1(nil, z0) -> nil
reverse(z0) -> appendreverse(z0, nil)

Types:
*' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c24 :: c5:c6:c7:c8:c9:c10:c11:c12:c13 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#MULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c5:c6:c7:c8:c9:c10:c11:c12:c13
+' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c25 :: c:c1:c2:c3:c4 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#ADD :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c:c1:c2:c3:c4
APPENDREVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c26
c26 :: c27:c28 -> c26
APPENDREVERSE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c27:c28
:: :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c27 :: c26 -> c27:c28
nil :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c28 :: c27:c28
BFTMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c29
c29 :: c30 -> c29
BFTMULT' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c30
tuple#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c30 :: c31 -> c32 -> c30
BFTMULT'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c31
bftMult'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
BFTMULT'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c32
c31 :: c33:c34 -> c31
BFTMULT'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c33:c34
c32 :: c43 -> c32
DEQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c43
c33 :: c35:c36 -> c33:c34
BFTMULT'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c35:c36
c34 :: c33:c34
leaf :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c35 :: c30 -> c35:c36
node :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c36 :: c37 -> c48 -> c48 -> c35:c36
BFTMULT'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c37
enqueue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
ENQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c48
c37 :: c30 -> c57 -> c37
matrixMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
MATRIXMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c57
COMPUTELINE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c38
c38 :: c39:c40 -> c38
COMPUTELINE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c39:c40
c39 :: c41:c42 -> c39:c40
COMPUTELINE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c41:c42
c40 :: c39:c40
c41 :: c38 -> c50 -> c41:c42
lineMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
LINEMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c50
c42 :: c41:c42
c43 :: c44:c45 -> c43
DEQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c44:c45
c44 :: c44:c45
c45 :: c46:c47 -> c61 -> c44:c45
DEQUEUE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c46:c47
reverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
REVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c61
c46 :: c46:c47
c47 :: c46:c47
c48 :: c49 -> c48
ENQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c49
c49 :: c49
c50 :: c51:c52 -> c50
LINEMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c51:c52
c51 :: c53:c54:c55:c56 -> c51:c52
LINEMULT#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c52 :: c51:c52
c53 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c54 :: c50 -> c53:c54:c55:c56
c55 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c56 :: c50 -> c53:c54:c55:c56
c57 :: c58:c59:c60 -> c57
MATRIXMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c58:c59:c60
c58 :: c38 -> c58:c59:c60
c59 :: c57 -> c58:c59:c60
c60 :: c58:c59:c60
c61 :: c26 -> c61
#0 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c :: c:c1:c2:c3:c4
#neg :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#s :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c1 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4
#PRED :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c16:c17:c18:c19
c2 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
#add :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#pos :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c3 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4
#SUCC :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c20:c21:c22:c23
c4 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
c5 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c6 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c7 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c8 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c9 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
#NATMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c14:c15
c10 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c11 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c12 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c13 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c14 :: c14:c15
c15 :: c:c1:c2:c3:c4 -> c14:c15 -> c14:c15
#natmult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c16 :: c16:c17:c18:c19
c17 :: c16:c17:c18:c19
c18 :: c16:c17:c18:c19
c19 :: c16:c17:c18:c19
c20 :: c20:c21:c22:c23
c21 :: c20:c21:c22:c23
c22 :: c20:c21:c22:c23
c23 :: c20:c21:c22:c23
#pred :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#succ :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#mult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
enqueue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
matrixMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos1_62 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c5:c6:c7:c8:c9:c10:c11:c12:c132_62 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
hole_c:c1:c2:c3:c43_62 :: c:c1:c2:c3:c4
hole_c264_62 :: c26
hole_c27:c285_62 :: c27:c28
hole_c296_62 :: c29
hole_c307_62 :: c30
hole_c318_62 :: c31
hole_c329_62 :: c32
hole_c33:c3410_62 :: c33:c34
hole_c4311_62 :: c43
hole_c35:c3612_62 :: c35:c36
hole_c3713_62 :: c37
hole_c4814_62 :: c48
hole_c5715_62 :: c57
hole_c3816_62 :: c38
hole_c39:c4017_62 :: c39:c40
hole_c41:c4218_62 :: c41:c42
hole_c5019_62 :: c50
hole_c44:c4520_62 :: c44:c45
hole_c46:c4721_62 :: c46:c47
hole_c6122_62 :: c61
hole_c4923_62 :: c49
hole_c51:c5224_62 :: c51:c52
hole_c53:c54:c55:c5625_62 :: c53:c54:c55:c56
hole_c58:c59:c6026_62 :: c58:c59:c60
hole_c16:c17:c18:c1927_62 :: c16:c17:c18:c19
hole_c20:c21:c22:c2328_62 :: c20:c21:c22:c23
hole_c14:c1529_62 :: c14:c15
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62 :: Nat -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
gen_c:c1:c2:c3:c431_62 :: Nat -> c:c1:c2:c3:c4
gen_c14:c1532_62 :: Nat -> c14:c15


Lemmas:
appendreverse#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n250_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n250_62, b)), rt in Omega(0)
LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n60901_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n60901_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n60901_62)
LINEMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62)) -> *33_62, rt in Omega(n30296_62)
lineMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n9704981_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n9704981_62)
lineMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n4908489_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0)) -> *33_62, rt in Omega(n4908489_62)
MATRIXMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14791201_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14791201_62)
MATRIXMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14779477_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14779477_62)
matrixMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14805808_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14805808_62), rt in Omega(0)


Generator Equations:
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0) <=> nil
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(x, 1)) <=> ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(x))
gen_c:c1:c2:c3:c431_62(0) <=> c
gen_c:c1:c2:c3:c431_62(+(x, 1)) <=> c2(c16, gen_c:c1:c2:c3:c431_62(x))
gen_c14:c1532_62(0) <=> c14
gen_c14:c1532_62(+(x, 1)) <=> c15(c, gen_c14:c1532_62(x))


The following defined symbols remain to be analysed:
matrixMult, APPENDREVERSE, APPENDREVERSE#1, BFTMULT', BFTMULT'#1, bftMult', bftMult'#1

They will be analysed ascendingly in the following order:
APPENDREVERSE = APPENDREVERSE#1
BFTMULT' = BFTMULT'#1
matrixMult < BFTMULT'#1
matrixMult < bftMult'#1
matrixMult = matrixMult#1
bftMult' = bftMult'#1

----------------------------------------

(39) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
APPENDREVERSE#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14811530_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14811530_62)

Induction Base:
APPENDREVERSE#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, 0)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))

Induction Step:
APPENDREVERSE#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, +(n14811530_62, 1))), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) ->_R^Omega(1)
c27(APPENDREVERSE(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14811530_62)), ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)))) ->_R^Omega(1)
c27(c26(APPENDREVERSE#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14811530_62)), ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))))) ->_IH
c27(c26(*33_62))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(40)
Obligation:
Innermost TRS:
Rules:
*'(z0, z1) -> c24(#MULT(z0, z1))
+'(z0, z1) -> c25(#ADD(z0, z1))
APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
APPENDREVERSE#1(nil, z0) -> c28
BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
BFTMULT'#3(nil, z0, z1) -> c34
BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
COMPUTELINE#1(nil, z0, z1) -> c40
COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
COMPUTELINE#2(nil, z0, z1, z2) -> c42
DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
DEQUEUE#1(::(z0, z1), z2) -> c44
DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
DEQUEUE#2(::(z0, z1)) -> c46
DEQUEUE#2(nil) -> c47
ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
LINEMULT#1(nil, z0, z1) -> c52
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*'(z3, z2), z0), *'(z3, z2))
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
MATRIXMULT#1(nil, z0) -> c60
REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))
#ADD(#0, z0) -> c
#ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
#ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
#ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#MULT(#0, #0) -> c5
#MULT(#0, #neg(z0)) -> c6
#MULT(#0, #pos(z0)) -> c7
#MULT(#neg(z0), #0) -> c8
#MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
#MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
#MULT(#pos(z0), #0) -> c11
#MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
#MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
#NATMULT(#0, z0) -> c14
#NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
#PRED(#0) -> c16
#PRED(#neg(#s(z0))) -> c17
#PRED(#pos(#s(#0))) -> c18
#PRED(#pos(#s(#s(z0)))) -> c19
#SUCC(#0) -> c20
#SUCC(#neg(#s(#0))) -> c21
#SUCC(#neg(#s(#s(z0)))) -> c22
#SUCC(#pos(#s(z0))) -> c23
#add(#0, z0) -> z0
#add(#neg(#s(#0)), z0) -> #pred(z0)
#add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
#add(#pos(#s(#0)), z0) -> #succ(z0)
#add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
#mult(#0, #0) -> #0
#mult(#0, #neg(z0)) -> #0
#mult(#0, #pos(z0)) -> #0
#mult(#neg(z0), #0) -> #0
#mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
#mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #0) -> #0
#mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
#natmult(#0, z0) -> #0
#natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
#pred(#0) -> #neg(#s(#0))
#pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
#pred(#pos(#s(#0))) -> #0
#pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
#succ(#0) -> #pos(#s(#0))
#succ(#neg(#s(#0))) -> #0
#succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
#succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
*'(z0, z1) -> #mult(z0, z1)
+'(z0, z1) -> #add(z0, z1)
appendreverse(z0, z1) -> appendreverse#1(z0, z1)
appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
appendreverse#1(nil, z0) -> z0
bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
bftMult'#3(nil, z0, z1) -> z0
bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
computeLine#1(nil, z0, z1) -> z0
computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
computeLine#2(nil, z0, z1, z2) -> nil
dequeue(z0, z1) -> dequeue#1(z0, z1)
dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
enqueue(z0, z1) -> enqueue#1(z1, z0)
enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
lineMult#1(nil, z0, z1) -> nil
lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+'(*'(z3, z2), z0), lineMult(z2, z4, z1))
lineMult#2(nil, z0, z1, z2) -> ::(*'(z1, z0), lineMult(z0, z2, nil))
matrixMult(z0, z1) -> matrixMult#1(z0, z1)
matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
matrixMult#1(nil, z0) -> nil
reverse(z0) -> appendreverse(z0, nil)

Types:
*' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c24 :: c5:c6:c7:c8:c9:c10:c11:c12:c13 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#MULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c5:c6:c7:c8:c9:c10:c11:c12:c13
+' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c25 :: c:c1:c2:c3:c4 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#ADD :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c:c1:c2:c3:c4
APPENDREVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c26
c26 :: c27:c28 -> c26
APPENDREVERSE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c27:c28
:: :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c27 :: c26 -> c27:c28
nil :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c28 :: c27:c28
BFTMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c29
c29 :: c30 -> c29
BFTMULT' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c30
tuple#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c30 :: c31 -> c32 -> c30
BFTMULT'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c31
bftMult'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
BFTMULT'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c32
c31 :: c33:c34 -> c31
BFTMULT'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c33:c34
c32 :: c43 -> c32
DEQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c43
c33 :: c35:c36 -> c33:c34
BFTMULT'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c35:c36
c34 :: c33:c34
leaf :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c35 :: c30 -> c35:c36
node :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c36 :: c37 -> c48 -> c48 -> c35:c36
BFTMULT'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c37
enqueue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
ENQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c48
c37 :: c30 -> c57 -> c37
matrixMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
MATRIXMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c57
COMPUTELINE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c38
c38 :: c39:c40 -> c38
COMPUTELINE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c39:c40
c39 :: c41:c42 -> c39:c40
COMPUTELINE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c41:c42
c40 :: c39:c40
c41 :: c38 -> c50 -> c41:c42
lineMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
LINEMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c50
c42 :: c41:c42
c43 :: c44:c45 -> c43
DEQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c44:c45
c44 :: c44:c45
c45 :: c46:c47 -> c61 -> c44:c45
DEQUEUE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c46:c47
reverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
REVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c61
c46 :: c46:c47
c47 :: c46:c47
c48 :: c49 -> c48
ENQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c49
c49 :: c49
c50 :: c51:c52 -> c50
LINEMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c51:c52
c51 :: c53:c54:c55:c56 -> c51:c52
LINEMULT#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c52 :: c51:c52
c53 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c54 :: c50 -> c53:c54:c55:c56
c55 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c56 :: c50 -> c53:c54:c55:c56
c57 :: c58:c59:c60 -> c57
MATRIXMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c58:c59:c60
c58 :: c38 -> c58:c59:c60
c59 :: c57 -> c58:c59:c60
c60 :: c58:c59:c60
c61 :: c26 -> c61
#0 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c :: c:c1:c2:c3:c4
#neg :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#s :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c1 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4
#PRED :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c16:c17:c18:c19
c2 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
#add :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#pos :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c3 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4
#SUCC :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c20:c21:c22:c23
c4 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
c5 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c6 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c7 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c8 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c9 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
#NATMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c14:c15
c10 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c11 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c12 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c13 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c14 :: c14:c15
c15 :: c:c1:c2:c3:c4 -> c14:c15 -> c14:c15
#natmult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c16 :: c16:c17:c18:c19
c17 :: c16:c17:c18:c19
c18 :: c16:c17:c18:c19
c19 :: c16:c17:c18:c19
c20 :: c20:c21:c22:c23
c21 :: c20:c21:c22:c23
c22 :: c20:c21:c22:c23
c23 :: c20:c21:c22:c23
#pred :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#succ :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#mult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
enqueue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
matrixMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos1_62 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c5:c6:c7:c8:c9:c10:c11:c12:c132_62 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
hole_c:c1:c2:c3:c43_62 :: c:c1:c2:c3:c4
hole_c264_62 :: c26
hole_c27:c285_62 :: c27:c28
hole_c296_62 :: c29
hole_c307_62 :: c30
hole_c318_62 :: c31
hole_c329_62 :: c32
hole_c33:c3410_62 :: c33:c34
hole_c4311_62 :: c43
hole_c35:c3612_62 :: c35:c36
hole_c3713_62 :: c37
hole_c4814_62 :: c48
hole_c5715_62 :: c57
hole_c3816_62 :: c38
hole_c39:c4017_62 :: c39:c40
hole_c41:c4218_62 :: c41:c42
hole_c5019_62 :: c50
hole_c44:c4520_62 :: c44:c45
hole_c46:c4721_62 :: c46:c47
hole_c6122_62 :: c61
hole_c4923_62 :: c49
hole_c51:c5224_62 :: c51:c52
hole_c53:c54:c55:c5625_62 :: c53:c54:c55:c56
hole_c58:c59:c6026_62 :: c58:c59:c60
hole_c16:c17:c18:c1927_62 :: c16:c17:c18:c19
hole_c20:c21:c22:c2328_62 :: c20:c21:c22:c23
hole_c14:c1529_62 :: c14:c15
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62 :: Nat -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
gen_c:c1:c2:c3:c431_62 :: Nat -> c:c1:c2:c3:c4
gen_c14:c1532_62 :: Nat -> c14:c15


Lemmas:
appendreverse#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n250_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n250_62, b)), rt in Omega(0)
LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n60901_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n60901_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n60901_62)
LINEMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62)) -> *33_62, rt in Omega(n30296_62)
lineMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n9704981_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n9704981_62)
lineMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n4908489_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0)) -> *33_62, rt in Omega(n4908489_62)
MATRIXMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14791201_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14791201_62)
MATRIXMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14779477_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14779477_62)
matrixMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14805808_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14805808_62), rt in Omega(0)
APPENDREVERSE#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14811530_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14811530_62)


Generator Equations:
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0) <=> nil
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(x, 1)) <=> ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(x))
gen_c:c1:c2:c3:c431_62(0) <=> c
gen_c:c1:c2:c3:c431_62(+(x, 1)) <=> c2(c16, gen_c:c1:c2:c3:c431_62(x))
gen_c14:c1532_62(0) <=> c14
gen_c14:c1532_62(+(x, 1)) <=> c15(c, gen_c14:c1532_62(x))


The following defined symbols remain to be analysed:
APPENDREVERSE

They will be analysed ascendingly in the following order:
APPENDREVERSE = APPENDREVERSE#1

----------------------------------------

(41) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
APPENDREVERSE(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14839545_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14839545_62)

Induction Base:
APPENDREVERSE(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))

Induction Step:
APPENDREVERSE(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n14839545_62, 1)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) ->_R^Omega(1)
c26(APPENDREVERSE#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n14839545_62, 1)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))) ->_R^Omega(1)
c26(c27(APPENDREVERSE(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14839545_62), ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))))) ->_IH
c26(c27(*33_62))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(42)
Obligation:
Innermost TRS:
Rules:
*'(z0, z1) -> c24(#MULT(z0, z1))
+'(z0, z1) -> c25(#ADD(z0, z1))
APPENDREVERSE(z0, z1) -> c26(APPENDREVERSE#1(z0, z1))
APPENDREVERSE#1(::(z0, z1), z2) -> c27(APPENDREVERSE(z1, ::(z0, z2)))
APPENDREVERSE#1(nil, z0) -> c28
BFTMULT(z0, z1) -> c29(BFTMULT'(tuple#2(::(z0, nil), nil), z1))
BFTMULT'(z0, z1) -> c30(BFTMULT'#1(bftMult'#2(z0), z1), BFTMULT'#2(z0))
BFTMULT'#1(tuple#2(z0, z1), z2) -> c31(BFTMULT'#3(z0, z2, z1))
BFTMULT'#2(tuple#2(z0, z1)) -> c32(DEQUEUE(z0, z1))
BFTMULT'#3(::(z0, z1), z2, z3) -> c33(BFTMULT'#4(z0, z2, z3))
BFTMULT'#3(nil, z0, z1) -> c34
BFTMULT'#4(leaf, z0, z1) -> c35(BFTMULT'(z1, z0))
BFTMULT'#4(node(z0, z1, z2), z3, z4) -> c36(BFTMULT'#5(enqueue(z2, enqueue(z1, z4)), z3, z0), ENQUEUE(z2, enqueue(z1, z4)), ENQUEUE(z1, z4))
BFTMULT'#5(z0, z1, z2) -> c37(BFTMULT'(z0, matrixMult(z1, z2)), MATRIXMULT(z1, z2))
COMPUTELINE(z0, z1, z2) -> c38(COMPUTELINE#1(z0, z2, z1))
COMPUTELINE#1(::(z0, z1), z2, z3) -> c39(COMPUTELINE#2(z3, z2, z0, z1))
COMPUTELINE#1(nil, z0, z1) -> c40
COMPUTELINE#2(::(z0, z1), z2, z3, z4) -> c41(COMPUTELINE(z4, z1, lineMult(z3, z0, z2)), LINEMULT(z3, z0, z2))
COMPUTELINE#2(nil, z0, z1, z2) -> c42
DEQUEUE(z0, z1) -> c43(DEQUEUE#1(z0, z1))
DEQUEUE#1(::(z0, z1), z2) -> c44
DEQUEUE#1(nil, z0) -> c45(DEQUEUE#2(reverse(z0)), REVERSE(z0))
DEQUEUE#2(::(z0, z1)) -> c46
DEQUEUE#2(nil) -> c47
ENQUEUE(z0, z1) -> c48(ENQUEUE#1(z1, z0))
ENQUEUE#1(tuple#2(z0, z1), z2) -> c49
LINEMULT(z0, z1, z2) -> c50(LINEMULT#1(z1, z2, z0))
LINEMULT#1(::(z0, z1), z2, z3) -> c51(LINEMULT#2(z2, z3, z0, z1))
LINEMULT#1(nil, z0, z1) -> c52
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c53(+'(*'(z3, z2), z0), *'(z3, z2))
LINEMULT#2(::(z0, z1), z2, z3, z4) -> c54(LINEMULT(z2, z4, z1))
LINEMULT#2(nil, z0, z1, z2) -> c55(*'(z1, z0))
LINEMULT#2(nil, z0, z1, z2) -> c56(LINEMULT(z0, z2, nil))
MATRIXMULT(z0, z1) -> c57(MATRIXMULT#1(z0, z1))
MATRIXMULT#1(::(z0, z1), z2) -> c58(COMPUTELINE(z0, z2, nil))
MATRIXMULT#1(::(z0, z1), z2) -> c59(MATRIXMULT(z1, z2))
MATRIXMULT#1(nil, z0) -> c60
REVERSE(z0) -> c61(APPENDREVERSE(z0, nil))
#ADD(#0, z0) -> c
#ADD(#neg(#s(#0)), z0) -> c1(#PRED(z0))
#ADD(#neg(#s(#s(z0))), z1) -> c2(#PRED(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#ADD(#pos(#s(#0)), z0) -> c3(#SUCC(z0))
#ADD(#pos(#s(#s(z0))), z1) -> c4(#SUCC(#add(#pos(#s(z0)), z1)), #ADD(#pos(#s(z0)), z1))
#MULT(#0, #0) -> c5
#MULT(#0, #neg(z0)) -> c6
#MULT(#0, #pos(z0)) -> c7
#MULT(#neg(z0), #0) -> c8
#MULT(#neg(z0), #neg(z1)) -> c9(#NATMULT(z0, z1))
#MULT(#neg(z0), #pos(z1)) -> c10(#NATMULT(z0, z1))
#MULT(#pos(z0), #0) -> c11
#MULT(#pos(z0), #neg(z1)) -> c12(#NATMULT(z0, z1))
#MULT(#pos(z0), #pos(z1)) -> c13(#NATMULT(z0, z1))
#NATMULT(#0, z0) -> c14
#NATMULT(#s(z0), z1) -> c15(#ADD(#pos(z1), #natmult(z0, z1)), #NATMULT(z0, z1))
#PRED(#0) -> c16
#PRED(#neg(#s(z0))) -> c17
#PRED(#pos(#s(#0))) -> c18
#PRED(#pos(#s(#s(z0)))) -> c19
#SUCC(#0) -> c20
#SUCC(#neg(#s(#0))) -> c21
#SUCC(#neg(#s(#s(z0)))) -> c22
#SUCC(#pos(#s(z0))) -> c23
#add(#0, z0) -> z0
#add(#neg(#s(#0)), z0) -> #pred(z0)
#add(#neg(#s(#s(z0))), z1) -> #pred(#add(#pos(#s(z0)), z1))
#add(#pos(#s(#0)), z0) -> #succ(z0)
#add(#pos(#s(#s(z0))), z1) -> #succ(#add(#pos(#s(z0)), z1))
#mult(#0, #0) -> #0
#mult(#0, #neg(z0)) -> #0
#mult(#0, #pos(z0)) -> #0
#mult(#neg(z0), #0) -> #0
#mult(#neg(z0), #neg(z1)) -> #pos(#natmult(z0, z1))
#mult(#neg(z0), #pos(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #0) -> #0
#mult(#pos(z0), #neg(z1)) -> #neg(#natmult(z0, z1))
#mult(#pos(z0), #pos(z1)) -> #pos(#natmult(z0, z1))
#natmult(#0, z0) -> #0
#natmult(#s(z0), z1) -> #add(#pos(z1), #natmult(z0, z1))
#pred(#0) -> #neg(#s(#0))
#pred(#neg(#s(z0))) -> #neg(#s(#s(z0)))
#pred(#pos(#s(#0))) -> #0
#pred(#pos(#s(#s(z0)))) -> #pos(#s(z0))
#succ(#0) -> #pos(#s(#0))
#succ(#neg(#s(#0))) -> #0
#succ(#neg(#s(#s(z0)))) -> #neg(#s(z0))
#succ(#pos(#s(z0))) -> #pos(#s(#s(z0)))
*'(z0, z1) -> #mult(z0, z1)
+'(z0, z1) -> #add(z0, z1)
appendreverse(z0, z1) -> appendreverse#1(z0, z1)
appendreverse#1(::(z0, z1), z2) -> appendreverse(z1, ::(z0, z2))
appendreverse#1(nil, z0) -> z0
bftMult(z0, z1) -> bftMult'(tuple#2(::(z0, nil), nil), z1)
bftMult'(z0, z1) -> bftMult'#1(bftMult'#2(z0), z1)
bftMult'#1(tuple#2(z0, z1), z2) -> bftMult'#3(z0, z2, z1)
bftMult'#2(tuple#2(z0, z1)) -> dequeue(z0, z1)
bftMult'#3(::(z0, z1), z2, z3) -> bftMult'#4(z0, z2, z3)
bftMult'#3(nil, z0, z1) -> z0
bftMult'#4(leaf, z0, z1) -> bftMult'(z1, z0)
bftMult'#4(node(z0, z1, z2), z3, z4) -> bftMult'#5(enqueue(z2, enqueue(z1, z4)), z3, z0)
bftMult'#5(z0, z1, z2) -> bftMult'(z0, matrixMult(z1, z2))
computeLine(z0, z1, z2) -> computeLine#1(z0, z2, z1)
computeLine#1(::(z0, z1), z2, z3) -> computeLine#2(z3, z2, z0, z1)
computeLine#1(nil, z0, z1) -> z0
computeLine#2(::(z0, z1), z2, z3, z4) -> computeLine(z4, z1, lineMult(z3, z0, z2))
computeLine#2(nil, z0, z1, z2) -> nil
dequeue(z0, z1) -> dequeue#1(z0, z1)
dequeue#1(::(z0, z1), z2) -> tuple#2(::(z0, nil), tuple#2(z1, z2))
dequeue#1(nil, z0) -> dequeue#2(reverse(z0))
dequeue#2(::(z0, z1)) -> tuple#2(::(z0, nil), tuple#2(z1, nil))
dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil))
enqueue(z0, z1) -> enqueue#1(z1, z0)
enqueue#1(tuple#2(z0, z1), z2) -> tuple#2(z0, ::(z2, z1))
lineMult(z0, z1, z2) -> lineMult#1(z1, z2, z0)
lineMult#1(::(z0, z1), z2, z3) -> lineMult#2(z2, z3, z0, z1)
lineMult#1(nil, z0, z1) -> nil
lineMult#2(::(z0, z1), z2, z3, z4) -> ::(+'(*'(z3, z2), z0), lineMult(z2, z4, z1))
lineMult#2(nil, z0, z1, z2) -> ::(*'(z1, z0), lineMult(z0, z2, nil))
matrixMult(z0, z1) -> matrixMult#1(z0, z1)
matrixMult#1(::(z0, z1), z2) -> ::(computeLine(z0, z2, nil), matrixMult(z1, z2))
matrixMult#1(nil, z0) -> nil
reverse(z0) -> appendreverse(z0, nil)

Types:
*' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c24 :: c5:c6:c7:c8:c9:c10:c11:c12:c13 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#MULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c5:c6:c7:c8:c9:c10:c11:c12:c13
+' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c25 :: c:c1:c2:c3:c4 -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#ADD :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c:c1:c2:c3:c4
APPENDREVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c26
c26 :: c27:c28 -> c26
APPENDREVERSE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c27:c28
:: :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c27 :: c26 -> c27:c28
nil :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c28 :: c27:c28
BFTMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c29
c29 :: c30 -> c29
BFTMULT' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c30
tuple#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c30 :: c31 -> c32 -> c30
BFTMULT'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c31
bftMult'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
BFTMULT'#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c32
c31 :: c33:c34 -> c31
BFTMULT'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c33:c34
c32 :: c43 -> c32
DEQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c43
c33 :: c35:c36 -> c33:c34
BFTMULT'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c35:c36
c34 :: c33:c34
leaf :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c35 :: c30 -> c35:c36
node :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c36 :: c37 -> c48 -> c48 -> c35:c36
BFTMULT'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c37
enqueue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
ENQUEUE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c48
c37 :: c30 -> c57 -> c37
matrixMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
MATRIXMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c57
COMPUTELINE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c38
c38 :: c39:c40 -> c38
COMPUTELINE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c39:c40
c39 :: c41:c42 -> c39:c40
COMPUTELINE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c41:c42
c40 :: c39:c40
c41 :: c38 -> c50 -> c41:c42
lineMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
LINEMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c50
c42 :: c41:c42
c43 :: c44:c45 -> c43
DEQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c44:c45
c44 :: c44:c45
c45 :: c46:c47 -> c61 -> c44:c45
DEQUEUE#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c46:c47
reverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
REVERSE :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c61
c46 :: c46:c47
c47 :: c46:c47
c48 :: c49 -> c48
ENQUEUE#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c49
c49 :: c49
c50 :: c51:c52 -> c50
LINEMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c51:c52
c51 :: c53:c54:c55:c56 -> c51:c52
LINEMULT#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c52 :: c51:c52
c53 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c54 :: c50 -> c53:c54:c55:c56
c55 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c53:c54:c55:c56
c56 :: c50 -> c53:c54:c55:c56
c57 :: c58:c59:c60 -> c57
MATRIXMULT#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c58:c59:c60
c58 :: c38 -> c58:c59:c60
c59 :: c57 -> c58:c59:c60
c60 :: c58:c59:c60
c61 :: c26 -> c61
#0 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c :: c:c1:c2:c3:c4
#neg :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#s :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c1 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4
#PRED :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c16:c17:c18:c19
c2 :: c16:c17:c18:c19 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
#add :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#pos :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c3 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4
#SUCC :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c20:c21:c22:c23
c4 :: c20:c21:c22:c23 -> c:c1:c2:c3:c4 -> c:c1:c2:c3:c4
c5 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c6 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c7 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c8 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c9 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
#NATMULT :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c14:c15
c10 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c11 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
c12 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c13 :: c14:c15 -> c5:c6:c7:c8:c9:c10:c11:c12:c13
c14 :: c14:c15
c15 :: c:c1:c2:c3:c4 -> c14:c15 -> c14:c15
#natmult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
c16 :: c16:c17:c18:c19
c17 :: c16:c17:c18:c19
c18 :: c16:c17:c18:c19
c19 :: c16:c17:c18:c19
c20 :: c20:c21:c22:c23
c21 :: c20:c21:c22:c23
c22 :: c20:c21:c22:c23
c23 :: c20:c21:c22:c23
#pred :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#succ :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
#mult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
appendreverse#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult' :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#3 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#4 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
bftMult'#5 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
computeLine#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
dequeue#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
enqueue#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
lineMult#2 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
matrixMult#1 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos1_62 :: c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
hole_c5:c6:c7:c8:c9:c10:c11:c12:c132_62 :: c5:c6:c7:c8:c9:c10:c11:c12:c13
hole_c:c1:c2:c3:c43_62 :: c:c1:c2:c3:c4
hole_c264_62 :: c26
hole_c27:c285_62 :: c27:c28
hole_c296_62 :: c29
hole_c307_62 :: c30
hole_c318_62 :: c31
hole_c329_62 :: c32
hole_c33:c3410_62 :: c33:c34
hole_c4311_62 :: c43
hole_c35:c3612_62 :: c35:c36
hole_c3713_62 :: c37
hole_c4814_62 :: c48
hole_c5715_62 :: c57
hole_c3816_62 :: c38
hole_c39:c4017_62 :: c39:c40
hole_c41:c4218_62 :: c41:c42
hole_c5019_62 :: c50
hole_c44:c4520_62 :: c44:c45
hole_c46:c4721_62 :: c46:c47
hole_c6122_62 :: c61
hole_c4923_62 :: c49
hole_c51:c5224_62 :: c51:c52
hole_c53:c54:c55:c5625_62 :: c53:c54:c55:c56
hole_c58:c59:c6026_62 :: c58:c59:c60
hole_c16:c17:c18:c1927_62 :: c16:c17:c18:c19
hole_c20:c21:c22:c2328_62 :: c20:c21:c22:c23
hole_c14:c1529_62 :: c14:c15
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62 :: Nat -> c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos
gen_c:c1:c2:c3:c431_62 :: Nat -> c:c1:c2:c3:c4
gen_c14:c1532_62 :: Nat -> c14:c15


Lemmas:
appendreverse#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n250_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(n250_62, b)), rt in Omega(0)
LINEMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n60901_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n60901_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n60901_62)
LINEMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n30296_62)) -> *33_62, rt in Omega(n30296_62)
lineMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n9704981_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(c)) -> *33_62, rt in Omega(n9704981_62)
lineMult(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(a), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n4908489_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0)) -> *33_62, rt in Omega(n4908489_62)
MATRIXMULT#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14791201_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14791201_62)
MATRIXMULT(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14779477_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14779477_62)
matrixMult#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14805808_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14805808_62), rt in Omega(0)
APPENDREVERSE#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14811530_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14811530_62)
APPENDREVERSE(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(n14839545_62), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14839545_62)


Generator Equations:
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(0) <=> nil
gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(x, 1)) <=> ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(x))
gen_c:c1:c2:c3:c431_62(0) <=> c
gen_c:c1:c2:c3:c431_62(+(x, 1)) <=> c2(c16, gen_c:c1:c2:c3:c431_62(x))
gen_c14:c1532_62(0) <=> c14
gen_c14:c1532_62(+(x, 1)) <=> c15(c, gen_c14:c1532_62(x))


The following defined symbols remain to be analysed:
APPENDREVERSE#1

They will be analysed ascendingly in the following order:
APPENDREVERSE = APPENDREVERSE#1

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(43) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
APPENDREVERSE#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14869769_62)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) -> *33_62, rt in Omega(n14869769_62)

Induction Base:
APPENDREVERSE#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, 0)), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))

Induction Step:
APPENDREVERSE#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, +(n14869769_62, 1))), gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)) ->_R^Omega(1)
c27(APPENDREVERSE(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14869769_62)), ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b)))) ->_R^Omega(1)
c27(c26(APPENDREVERSE#1(gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(+(1, n14869769_62)), ::(nil, gen_c24:c25::::nil:tuple#2:leaf:node:#0:#s:#neg:#pos30_62(b))))) ->_IH
c27(c26(*33_62))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
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(44)
BOUNDS(1, INF)