WORST_CASE(?,O(n^1))
proof of input_9fP3MqTuLT.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


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

(0) CpxTRS
(1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(2) CdtProblem
(3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
(4) CdtProblem
(5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CdtProblem
(7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CdtProblem
(9) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(10) CpxRelTRS
(11) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(12) CpxWeightedTrs
(13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
(14) CpxTypedWeightedTrs
(15) CompletionProof [UPPER BOUND(ID), 0 ms]
(16) CpxTypedWeightedCompleteTrs
(17) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
(18) CpxTypedWeightedCompleteTrs
(19) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
(20) CpxRNTS
(21) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
(22) CpxRNTS
(23) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
(24) CpxRNTS
(25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(26) CpxRNTS
(27) IntTrsBoundProof [UPPER BOUND(ID), 158 ms]
(28) CpxRNTS
(29) IntTrsBoundProof [UPPER BOUND(ID), 73 ms]
(30) CpxRNTS
(31) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(32) CpxRNTS
(33) IntTrsBoundProof [UPPER BOUND(ID), 5346 ms]
(34) CpxRNTS
(35) IntTrsBoundProof [UPPER BOUND(ID), 2661 ms]
(36) CpxRNTS
(37) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(38) CpxRNTS
(39) IntTrsBoundProof [UPPER BOUND(ID), 148 ms]
(40) CpxRNTS
(41) IntTrsBoundProof [UPPER BOUND(ID), 12 ms]
(42) CpxRNTS
(43) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(44) CpxRNTS
(45) IntTrsBoundProof [UPPER BOUND(ID), 198 ms]
(46) CpxRNTS
(47) IntTrsBoundProof [UPPER BOUND(ID), 22 ms]
(48) CpxRNTS
(49) FinalProof [FINISHED, 0 ms]
(50) BOUNDS(1, n^1)


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

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


The TRS R consists of the following rules:

   cond1(true, x, y) -> cond2(gr(y, 0), x, y)
   cond2(true, x, y) -> cond2(gr(y, 0), x, p(y))
   cond2(false, x, y) -> cond1(gr(x, 0), p(x), y)
   gr(0, x) -> false
   gr(s(x), 0) -> true
   gr(s(x), s(y)) -> gr(x, y)
   p(0) -> 0
   p(s(x)) -> x

S is empty.
Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

(1) CpxTrsToCdtProof (UPPER BOUND(ID))
Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT
----------------------------------------

(2)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   cond1(true, z0, z1) -> cond2(gr(z1, 0), z0, z1)
   cond2(true, z0, z1) -> cond2(gr(z1, 0), z0, p(z1))
   cond2(false, z0, z1) -> cond1(gr(z0, 0), p(z0), z1)
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   p(0) -> 0
   p(s(z0)) -> z0
Tuples:
   COND1(true, z0, z1) -> c(COND2(gr(z1, 0), z0, z1), GR(z1, 0))
   COND2(true, z0, z1) -> c1(COND2(gr(z1, 0), z0, p(z1)), GR(z1, 0))
   COND2(true, z0, z1) -> c2(COND2(gr(z1, 0), z0, p(z1)), P(z1))
   COND2(false, z0, z1) -> c3(COND1(gr(z0, 0), p(z0), z1), GR(z0, 0))
   COND2(false, z0, z1) -> c4(COND1(gr(z0, 0), p(z0), z1), P(z0))
   GR(0, z0) -> c5
   GR(s(z0), 0) -> c6
   GR(s(z0), s(z1)) -> c7(GR(z0, z1))
   P(0) -> c8
   P(s(z0)) -> c9
S tuples:
   COND1(true, z0, z1) -> c(COND2(gr(z1, 0), z0, z1), GR(z1, 0))
   COND2(true, z0, z1) -> c1(COND2(gr(z1, 0), z0, p(z1)), GR(z1, 0))
   COND2(true, z0, z1) -> c2(COND2(gr(z1, 0), z0, p(z1)), P(z1))
   COND2(false, z0, z1) -> c3(COND1(gr(z0, 0), p(z0), z1), GR(z0, 0))
   COND2(false, z0, z1) -> c4(COND1(gr(z0, 0), p(z0), z1), P(z0))
   GR(0, z0) -> c5
   GR(s(z0), 0) -> c6
   GR(s(z0), s(z1)) -> c7(GR(z0, z1))
   P(0) -> c8
   P(s(z0)) -> c9
K tuples:none
Defined Rule Symbols:   cond1_3, cond2_3, gr_2, p_1

Defined Pair Symbols:   COND1_3, COND2_3, GR_2, P_1

Compound Symbols:   c_2, c1_2, c2_2, c3_2, c4_2, c5, c6, c7_1, c8, c9


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

(3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing nodes:
   P(0) -> c8
   P(s(z0)) -> c9
   GR(0, z0) -> c5
   GR(s(z0), 0) -> c6

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

(4)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   cond1(true, z0, z1) -> cond2(gr(z1, 0), z0, z1)
   cond2(true, z0, z1) -> cond2(gr(z1, 0), z0, p(z1))
   cond2(false, z0, z1) -> cond1(gr(z0, 0), p(z0), z1)
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   p(0) -> 0
   p(s(z0)) -> z0
Tuples:
   COND1(true, z0, z1) -> c(COND2(gr(z1, 0), z0, z1), GR(z1, 0))
   COND2(true, z0, z1) -> c1(COND2(gr(z1, 0), z0, p(z1)), GR(z1, 0))
   COND2(true, z0, z1) -> c2(COND2(gr(z1, 0), z0, p(z1)), P(z1))
   COND2(false, z0, z1) -> c3(COND1(gr(z0, 0), p(z0), z1), GR(z0, 0))
   COND2(false, z0, z1) -> c4(COND1(gr(z0, 0), p(z0), z1), P(z0))
   GR(s(z0), s(z1)) -> c7(GR(z0, z1))
S tuples:
   COND1(true, z0, z1) -> c(COND2(gr(z1, 0), z0, z1), GR(z1, 0))
   COND2(true, z0, z1) -> c1(COND2(gr(z1, 0), z0, p(z1)), GR(z1, 0))
   COND2(true, z0, z1) -> c2(COND2(gr(z1, 0), z0, p(z1)), P(z1))
   COND2(false, z0, z1) -> c3(COND1(gr(z0, 0), p(z0), z1), GR(z0, 0))
   COND2(false, z0, z1) -> c4(COND1(gr(z0, 0), p(z0), z1), P(z0))
   GR(s(z0), s(z1)) -> c7(GR(z0, z1))
K tuples:none
Defined Rule Symbols:   cond1_3, cond2_3, gr_2, p_1

Defined Pair Symbols:   COND1_3, COND2_3, GR_2

Compound Symbols:   c_2, c1_2, c2_2, c3_2, c4_2, c7_1


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

(5) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 5 trailing tuple parts
----------------------------------------

(6)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   cond1(true, z0, z1) -> cond2(gr(z1, 0), z0, z1)
   cond2(true, z0, z1) -> cond2(gr(z1, 0), z0, p(z1))
   cond2(false, z0, z1) -> cond1(gr(z0, 0), p(z0), z1)
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   p(0) -> 0
   p(s(z0)) -> z0
Tuples:
   GR(s(z0), s(z1)) -> c7(GR(z0, z1))
   COND1(true, z0, z1) -> c(COND2(gr(z1, 0), z0, z1))
   COND2(true, z0, z1) -> c1(COND2(gr(z1, 0), z0, p(z1)))
   COND2(true, z0, z1) -> c2(COND2(gr(z1, 0), z0, p(z1)))
   COND2(false, z0, z1) -> c3(COND1(gr(z0, 0), p(z0), z1))
   COND2(false, z0, z1) -> c4(COND1(gr(z0, 0), p(z0), z1))
S tuples:
   GR(s(z0), s(z1)) -> c7(GR(z0, z1))
   COND1(true, z0, z1) -> c(COND2(gr(z1, 0), z0, z1))
   COND2(true, z0, z1) -> c1(COND2(gr(z1, 0), z0, p(z1)))
   COND2(true, z0, z1) -> c2(COND2(gr(z1, 0), z0, p(z1)))
   COND2(false, z0, z1) -> c3(COND1(gr(z0, 0), p(z0), z1))
   COND2(false, z0, z1) -> c4(COND1(gr(z0, 0), p(z0), z1))
K tuples:none
Defined Rule Symbols:   cond1_3, cond2_3, gr_2, p_1

Defined Pair Symbols:   GR_2, COND1_3, COND2_3

Compound Symbols:   c7_1, c_1, c1_1, c2_1, c3_1, c4_1


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

(7) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   cond1(true, z0, z1) -> cond2(gr(z1, 0), z0, z1)
   cond2(true, z0, z1) -> cond2(gr(z1, 0), z0, p(z1))
   cond2(false, z0, z1) -> cond1(gr(z0, 0), p(z0), z1)
   gr(s(z0), s(z1)) -> gr(z0, z1)

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

(8)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   p(0) -> 0
   p(s(z0)) -> z0
Tuples:
   GR(s(z0), s(z1)) -> c7(GR(z0, z1))
   COND1(true, z0, z1) -> c(COND2(gr(z1, 0), z0, z1))
   COND2(true, z0, z1) -> c1(COND2(gr(z1, 0), z0, p(z1)))
   COND2(true, z0, z1) -> c2(COND2(gr(z1, 0), z0, p(z1)))
   COND2(false, z0, z1) -> c3(COND1(gr(z0, 0), p(z0), z1))
   COND2(false, z0, z1) -> c4(COND1(gr(z0, 0), p(z0), z1))
S tuples:
   GR(s(z0), s(z1)) -> c7(GR(z0, z1))
   COND1(true, z0, z1) -> c(COND2(gr(z1, 0), z0, z1))
   COND2(true, z0, z1) -> c1(COND2(gr(z1, 0), z0, p(z1)))
   COND2(true, z0, z1) -> c2(COND2(gr(z1, 0), z0, p(z1)))
   COND2(false, z0, z1) -> c3(COND1(gr(z0, 0), p(z0), z1))
   COND2(false, z0, z1) -> c4(COND1(gr(z0, 0), p(z0), z1))
K tuples:none
Defined Rule Symbols:   gr_2, p_1

Defined Pair Symbols:   GR_2, COND1_3, COND2_3

Compound Symbols:   c7_1, c_1, c1_1, c2_1, c3_1, c4_1


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

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

(10)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

   GR(s(z0), s(z1)) -> c7(GR(z0, z1))
   COND1(true, z0, z1) -> c(COND2(gr(z1, 0), z0, z1))
   COND2(true, z0, z1) -> c1(COND2(gr(z1, 0), z0, p(z1)))
   COND2(true, z0, z1) -> c2(COND2(gr(z1, 0), z0, p(z1)))
   COND2(false, z0, z1) -> c3(COND1(gr(z0, 0), p(z0), z1))
   COND2(false, z0, z1) -> c4(COND1(gr(z0, 0), p(z0), z1))

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

   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   p(0) -> 0
   p(s(z0)) -> z0

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

(11) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(12)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

   GR(s(z0), s(z1)) -> c7(GR(z0, z1)) [1]
   COND1(true, z0, z1) -> c(COND2(gr(z1, 0), z0, z1)) [1]
   COND2(true, z0, z1) -> c1(COND2(gr(z1, 0), z0, p(z1))) [1]
   COND2(true, z0, z1) -> c2(COND2(gr(z1, 0), z0, p(z1))) [1]
   COND2(false, z0, z1) -> c3(COND1(gr(z0, 0), p(z0), z1)) [1]
   COND2(false, z0, z1) -> c4(COND1(gr(z0, 0), p(z0), z1)) [1]
   gr(0, z0) -> false [0]
   gr(s(z0), 0) -> true [0]
   p(0) -> 0 [0]
   p(s(z0)) -> z0 [0]

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

(13) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(14)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   GR(s(z0), s(z1)) -> c7(GR(z0, z1)) [1]
   COND1(true, z0, z1) -> c(COND2(gr(z1, 0), z0, z1)) [1]
   COND2(true, z0, z1) -> c1(COND2(gr(z1, 0), z0, p(z1))) [1]
   COND2(true, z0, z1) -> c2(COND2(gr(z1, 0), z0, p(z1))) [1]
   COND2(false, z0, z1) -> c3(COND1(gr(z0, 0), p(z0), z1)) [1]
   COND2(false, z0, z1) -> c4(COND1(gr(z0, 0), p(z0), z1)) [1]
   gr(0, z0) -> false [0]
   gr(s(z0), 0) -> true [0]
   p(0) -> 0 [0]
   p(s(z0)) -> z0 [0]

The TRS has the following type information:
GR :: s:0 -> s:0 -> c7
s :: s:0 -> s:0
c7 :: c7 -> c7
COND1 :: true:false -> s:0 -> s:0 -> c
true :: true:false
c :: c1:c2:c3:c4 -> c
COND2 :: true:false -> s:0 -> s:0 -> c1:c2:c3:c4
gr :: s:0 -> s:0 -> true:false
0 :: s:0
c1 :: c1:c2:c3:c4 -> c1:c2:c3:c4
p :: s:0 -> s:0
c2 :: c1:c2:c3:c4 -> c1:c2:c3:c4
false :: true:false
c3 :: c -> c1:c2:c3:c4
c4 :: c -> c1:c2:c3:c4

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

(15) CompletionProof (UPPER BOUND(ID))
The transformation into a RNTS is sound, since:

(a) The obligation is a constructor system where every type has a constant constructor,

(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:

   GR_2
   COND1_3
   COND2_3

(c) The following functions are completely defined:

   gr_2
   p_1

Due to the following rules being added:

   gr(v0, v1) -> null_gr [0]
   p(v0) -> 0 [0]

And the following fresh constants:    null_gr, const, const1, const2

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

(16)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   GR(s(z0), s(z1)) -> c7(GR(z0, z1)) [1]
   COND1(true, z0, z1) -> c(COND2(gr(z1, 0), z0, z1)) [1]
   COND2(true, z0, z1) -> c1(COND2(gr(z1, 0), z0, p(z1))) [1]
   COND2(true, z0, z1) -> c2(COND2(gr(z1, 0), z0, p(z1))) [1]
   COND2(false, z0, z1) -> c3(COND1(gr(z0, 0), p(z0), z1)) [1]
   COND2(false, z0, z1) -> c4(COND1(gr(z0, 0), p(z0), z1)) [1]
   gr(0, z0) -> false [0]
   gr(s(z0), 0) -> true [0]
   p(0) -> 0 [0]
   p(s(z0)) -> z0 [0]
   gr(v0, v1) -> null_gr [0]
   p(v0) -> 0 [0]

The TRS has the following type information:
GR :: s:0 -> s:0 -> c7
s :: s:0 -> s:0
c7 :: c7 -> c7
COND1 :: true:false:null_gr -> s:0 -> s:0 -> c
true :: true:false:null_gr
c :: c1:c2:c3:c4 -> c
COND2 :: true:false:null_gr -> s:0 -> s:0 -> c1:c2:c3:c4
gr :: s:0 -> s:0 -> true:false:null_gr
0 :: s:0
c1 :: c1:c2:c3:c4 -> c1:c2:c3:c4
p :: s:0 -> s:0
c2 :: c1:c2:c3:c4 -> c1:c2:c3:c4
false :: true:false:null_gr
c3 :: c -> c1:c2:c3:c4
c4 :: c -> c1:c2:c3:c4
null_gr :: true:false:null_gr
const :: c7
const1 :: c
const2 :: c1:c2:c3:c4

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

(17) NarrowingProof (BOTH BOUNDS(ID, ID))
Narrowed the inner basic terms of all right-hand sides by a single narrowing step.
----------------------------------------

(18)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   GR(s(z0), s(z1)) -> c7(GR(z0, z1)) [1]
   COND1(true, z0, 0) -> c(COND2(false, z0, 0)) [1]
   COND1(true, z0, s(z0')) -> c(COND2(true, z0, s(z0'))) [1]
   COND1(true, z0, z1) -> c(COND2(null_gr, z0, z1)) [1]
   COND2(true, z0, 0) -> c1(COND2(false, z0, 0)) [1]
   COND2(true, z0, 0) -> c1(COND2(false, z0, 0)) [1]
   COND2(true, z0, s(z0'')) -> c1(COND2(true, z0, z0'')) [1]
   COND2(true, z0, s(z0'')) -> c1(COND2(true, z0, 0)) [1]
   COND2(true, z0, 0) -> c1(COND2(null_gr, z0, 0)) [1]
   COND2(true, z0, s(z01)) -> c1(COND2(null_gr, z0, z01)) [1]
   COND2(true, z0, z1) -> c1(COND2(null_gr, z0, 0)) [1]
   COND2(true, z0, 0) -> c2(COND2(false, z0, 0)) [1]
   COND2(true, z0, 0) -> c2(COND2(false, z0, 0)) [1]
   COND2(true, z0, s(z02)) -> c2(COND2(true, z0, z02)) [1]
   COND2(true, z0, s(z02)) -> c2(COND2(true, z0, 0)) [1]
   COND2(true, z0, 0) -> c2(COND2(null_gr, z0, 0)) [1]
   COND2(true, z0, s(z03)) -> c2(COND2(null_gr, z0, z03)) [1]
   COND2(true, z0, z1) -> c2(COND2(null_gr, z0, 0)) [1]
   COND2(false, 0, z1) -> c3(COND1(false, 0, z1)) [1]
   COND2(false, 0, z1) -> c3(COND1(false, 0, z1)) [1]
   COND2(false, s(z04), z1) -> c3(COND1(true, z04, z1)) [1]
   COND2(false, s(z04), z1) -> c3(COND1(true, 0, z1)) [1]
   COND2(false, 0, z1) -> c3(COND1(null_gr, 0, z1)) [1]
   COND2(false, s(z05), z1) -> c3(COND1(null_gr, z05, z1)) [1]
   COND2(false, z0, z1) -> c3(COND1(null_gr, 0, z1)) [1]
   COND2(false, 0, z1) -> c4(COND1(false, 0, z1)) [1]
   COND2(false, 0, z1) -> c4(COND1(false, 0, z1)) [1]
   COND2(false, s(z06), z1) -> c4(COND1(true, z06, z1)) [1]
   COND2(false, s(z06), z1) -> c4(COND1(true, 0, z1)) [1]
   COND2(false, 0, z1) -> c4(COND1(null_gr, 0, z1)) [1]
   COND2(false, s(z07), z1) -> c4(COND1(null_gr, z07, z1)) [1]
   COND2(false, z0, z1) -> c4(COND1(null_gr, 0, z1)) [1]
   gr(0, z0) -> false [0]
   gr(s(z0), 0) -> true [0]
   p(0) -> 0 [0]
   p(s(z0)) -> z0 [0]
   gr(v0, v1) -> null_gr [0]
   p(v0) -> 0 [0]

The TRS has the following type information:
GR :: s:0 -> s:0 -> c7
s :: s:0 -> s:0
c7 :: c7 -> c7
COND1 :: true:false:null_gr -> s:0 -> s:0 -> c
true :: true:false:null_gr
c :: c1:c2:c3:c4 -> c
COND2 :: true:false:null_gr -> s:0 -> s:0 -> c1:c2:c3:c4
gr :: s:0 -> s:0 -> true:false:null_gr
0 :: s:0
c1 :: c1:c2:c3:c4 -> c1:c2:c3:c4
p :: s:0 -> s:0
c2 :: c1:c2:c3:c4 -> c1:c2:c3:c4
false :: true:false:null_gr
c3 :: c -> c1:c2:c3:c4
c4 :: c -> c1:c2:c3:c4
null_gr :: true:false:null_gr
const :: c7
const1 :: c
const2 :: c1:c2:c3:c4

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

(19) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   true => 2
   0 => 0
   false => 1
   null_gr => 0
   const => 0
   const1 => 0
   const2 => 0

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

(20)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, z0, 1 + z0') :|: z = 2, z0' >= 0, z0 >= 0, z'' = 1 + z0', z' = z0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, z0, 0) :|: z = 2, z'' = 0, z0 >= 0, z' = z0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z0, z0'') :|: z = 2, z'' = 1 + z0'', z0 >= 0, z0'' >= 0, z' = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z0, z02) :|: z = 2, z02 >= 0, z0 >= 0, z' = z0, z'' = 1 + z02
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z0, 0) :|: z = 2, z'' = 1 + z0'', z0 >= 0, z0'' >= 0, z' = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z0, 0) :|: z = 2, z02 >= 0, z0 >= 0, z' = z0, z'' = 1 + z02
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(1, z0, 0) :|: z = 2, z'' = 0, z0 >= 0, z' = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z0, z01) :|: z = 2, z01 >= 0, z0 >= 0, z' = z0, z'' = 1 + z01
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z0, z03) :|: z = 2, z'' = 1 + z03, z0 >= 0, z03 >= 0, z' = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z0, 0) :|: z = 2, z'' = 0, z0 >= 0, z' = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z0, 0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, z04, z1) :|: z04 >= 0, z1 >= 0, z = 1, z' = 1 + z04, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, z06, z1) :|: z1 >= 0, z = 1, z06 >= 0, z' = 1 + z06, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z1) :|: z04 >= 0, z1 >= 0, z = 1, z' = 1 + z04, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z1) :|: z1 >= 0, z = 1, z06 >= 0, z' = 1 + z06, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z1) :|: z1 >= 0, z = 1, z' = 0, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z05, z1) :|: z1 >= 0, z = 1, z05 >= 0, z' = 1 + z05, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z07, z1) :|: z1 >= 0, z07 >= 0, z = 1, z' = 1 + z07, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z1) :|: z1 >= 0, z = 1, z' = 0, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   GR(z, z') -{ 1 }-> 1 + GR(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   gr(z, z') -{ 0 }-> 2 :|: z = 1 + z0, z0 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z0 >= 0, z = 0, z' = z0
   gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   p(z) -{ 0 }-> z0 :|: z = 1 + z0, z0 >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0


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

(21) SimplificationProof (BOTH BOUNDS(ID, ID))
Simplified the RNTS by moving equalities from the constraints into the right-hand sides.
----------------------------------------

(22)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0


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

(23) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID))
Found the following analysis order by SCC decomposition:

   { GR }
   { COND2, COND1 }
   { p }
   { gr }

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

(24)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {GR}, {COND2,COND1}, {p}, {gr}

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

(25) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(26)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {GR}, {COND2,COND1}, {p}, {gr}

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

(27) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: GR
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

(28)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {GR}, {COND2,COND1}, {p}, {gr}
Previous analysis results are:
  GR: runtime: ?, size: O(1) [0]

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

(29) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: GR
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z'

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

(30)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {COND2,COND1}, {p}, {gr}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]

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

(31) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(32)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {COND2,COND1}, {p}, {gr}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]

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

(33) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: COND2
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

Computed SIZE bound using CoFloCo for: COND1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

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

(34)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {COND2,COND1}, {p}, {gr}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  COND2: runtime: ?, size: O(1) [0]
  COND1: runtime: ?, size: O(1) [1]

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

(35) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: COND2
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 12 + 2*z' + z''

Computed RUNTIME bound using CoFloCo for: COND1
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 13 + 2*z' + z''

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

(36)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z', 0) :|: z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(2, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(1, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', 0) :|: z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'' - 1) :|: z = 2, z'' - 1 >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {p}, {gr}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  COND2: runtime: O(n^1) [12 + 2*z' + z''], size: O(1) [0]
  COND1: runtime: O(n^1) [13 + 2*z' + z''], size: O(1) [1]

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

(37) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(38)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'') -{ 13 + 2*z' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   COND1(z, z', z'') -{ 13 + 2*z' + z'' }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   COND1(z, z', z'') -{ 13 + 2*z' + z'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s10 :|: s10 >= 0, s10 <= 1, z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s11 :|: s11 >= 0, s11 <= 1, z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s12 :|: s12 >= 0, s12 <= 1, z'' >= 0, z = 1, z' - 1 >= 0
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s13 :|: s13 >= 0, s13 <= 1, z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s8 :|: s8 >= 0, s8 <= 1, z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s9 :|: s9 >= 0, s9 <= 1, z' - 1 >= 0, z'' >= 0, z = 1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {p}, {gr}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  COND2: runtime: O(n^1) [12 + 2*z' + z''], size: O(1) [0]
  COND1: runtime: O(n^1) [13 + 2*z' + z''], size: O(1) [1]

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

(39) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: p
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

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

(40)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'') -{ 13 + 2*z' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   COND1(z, z', z'') -{ 13 + 2*z' + z'' }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   COND1(z, z', z'') -{ 13 + 2*z' + z'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s10 :|: s10 >= 0, s10 <= 1, z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s11 :|: s11 >= 0, s11 <= 1, z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s12 :|: s12 >= 0, s12 <= 1, z'' >= 0, z = 1, z' - 1 >= 0
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s13 :|: s13 >= 0, s13 <= 1, z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s8 :|: s8 >= 0, s8 <= 1, z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s9 :|: s9 >= 0, s9 <= 1, z' - 1 >= 0, z'' >= 0, z = 1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {p}, {gr}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  COND2: runtime: O(n^1) [12 + 2*z' + z''], size: O(1) [0]
  COND1: runtime: O(n^1) [13 + 2*z' + z''], size: O(1) [1]
  p: runtime: ?, size: O(n^1) [z]

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

(41) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: p
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

(42)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'') -{ 13 + 2*z' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   COND1(z, z', z'') -{ 13 + 2*z' + z'' }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   COND1(z, z', z'') -{ 13 + 2*z' + z'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s10 :|: s10 >= 0, s10 <= 1, z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s11 :|: s11 >= 0, s11 <= 1, z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s12 :|: s12 >= 0, s12 <= 1, z'' >= 0, z = 1, z' - 1 >= 0
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s13 :|: s13 >= 0, s13 <= 1, z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s8 :|: s8 >= 0, s8 <= 1, z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s9 :|: s9 >= 0, s9 <= 1, z' - 1 >= 0, z'' >= 0, z = 1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {gr}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  COND2: runtime: O(n^1) [12 + 2*z' + z''], size: O(1) [0]
  COND1: runtime: O(n^1) [13 + 2*z' + z''], size: O(1) [1]
  p: runtime: O(1) [0], size: O(n^1) [z]

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

(43) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(44)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'') -{ 13 + 2*z' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   COND1(z, z', z'') -{ 13 + 2*z' + z'' }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   COND1(z, z', z'') -{ 13 + 2*z' + z'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s10 :|: s10 >= 0, s10 <= 1, z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s11 :|: s11 >= 0, s11 <= 1, z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s12 :|: s12 >= 0, s12 <= 1, z'' >= 0, z = 1, z' - 1 >= 0
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s13 :|: s13 >= 0, s13 <= 1, z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s8 :|: s8 >= 0, s8 <= 1, z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s9 :|: s9 >= 0, s9 <= 1, z' - 1 >= 0, z'' >= 0, z = 1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {gr}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  COND2: runtime: O(n^1) [12 + 2*z' + z''], size: O(1) [0]
  COND1: runtime: O(n^1) [13 + 2*z' + z''], size: O(1) [1]
  p: runtime: O(1) [0], size: O(n^1) [z]

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

(45) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: gr
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

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

(46)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'') -{ 13 + 2*z' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   COND1(z, z', z'') -{ 13 + 2*z' + z'' }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   COND1(z, z', z'') -{ 13 + 2*z' + z'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s10 :|: s10 >= 0, s10 <= 1, z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s11 :|: s11 >= 0, s11 <= 1, z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s12 :|: s12 >= 0, s12 <= 1, z'' >= 0, z = 1, z' - 1 >= 0
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s13 :|: s13 >= 0, s13 <= 1, z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s8 :|: s8 >= 0, s8 <= 1, z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s9 :|: s9 >= 0, s9 <= 1, z' - 1 >= 0, z'' >= 0, z = 1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {gr}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  COND2: runtime: O(n^1) [12 + 2*z' + z''], size: O(1) [0]
  COND1: runtime: O(n^1) [13 + 2*z' + z''], size: O(1) [1]
  p: runtime: O(1) [0], size: O(n^1) [z]
  gr: runtime: ?, size: O(1) [2]

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

(47) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: gr
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

(48)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'') -{ 13 + 2*z' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 2, z'' = 0, z' >= 0
   COND1(z, z', z'') -{ 13 + 2*z' + z'' }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   COND1(z, z', z'') -{ 13 + 2*z' + z'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s10 :|: s10 >= 0, s10 <= 1, z' - 1 >= 0, z'' >= 0, z = 1
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s11 :|: s11 >= 0, s11 <= 1, z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s12 :|: s12 >= 0, s12 <= 1, z'' >= 0, z = 1, z' - 1 >= 0
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s13 :|: s13 >= 0, s13 <= 1, z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 2, z' >= 0, z'' - 1 >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 2, z'' = 0, z' >= 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' - 1 >= 0, z' >= 0
   COND2(z, z', z'') -{ 13 + 2*z' }-> 1 + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 14 + z'' }-> 1 + s8 :|: s8 >= 0, s8 <= 1, z'' >= 0, z = 1, z' = 0
   COND2(z, z', z'') -{ 12 + 2*z' + z'' }-> 1 + s9 :|: s9 >= 0, s9 <= 1, z' - 1 >= 0, z'' >= 0, z = 1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: 
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  COND2: runtime: O(n^1) [12 + 2*z' + z''], size: O(1) [0]
  COND1: runtime: O(n^1) [13 + 2*z' + z''], size: O(1) [1]
  p: runtime: O(1) [0], size: O(n^1) [z]
  gr: runtime: O(1) [0], size: O(1) [2]

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

(49) FinalProof (FINISHED)
Computed overall runtime complexity
----------------------------------------

(50)
BOUNDS(1, n^1)