WORST_CASE(Omega(n^1),O(n^2))
proof of /export/starexec/sandbox/benchmark/theBenchmark.trs
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

(0) CpxRelTRS
(1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 919 ms]
(2) CpxRelTRS
(3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(4) CpxWeightedTrs
    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CpxTypedWeightedTrs
    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
    (8) CpxTypedWeightedCompleteTrs
    (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CpxTypedWeightedCompleteTrs
    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 5 ms]
    (12) CpxRNTS
    (13) InliningProof [UPPER BOUND(ID), 889 ms]
    (14) CpxRNTS
    (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (16) CpxRNTS
    (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 3 ms]
    (18) CpxRNTS
    (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (20) CpxRNTS
    (21) IntTrsBoundProof [UPPER BOUND(ID), 152 ms]
    (22) CpxRNTS
    (23) IntTrsBoundProof [UPPER BOUND(ID), 56 ms]
    (24) CpxRNTS
    (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (26) CpxRNTS
    (27) IntTrsBoundProof [UPPER BOUND(ID), 414 ms]
    (28) CpxRNTS
    (29) IntTrsBoundProof [UPPER BOUND(ID), 114 ms]
    (30) CpxRNTS
    (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (32) CpxRNTS
    (33) IntTrsBoundProof [UPPER BOUND(ID), 264 ms]
    (34) CpxRNTS
    (35) IntTrsBoundProof [UPPER BOUND(ID), 76 ms]
    (36) CpxRNTS
    (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (38) CpxRNTS
    (39) IntTrsBoundProof [UPPER BOUND(ID), 152 ms]
    (40) CpxRNTS
    (41) IntTrsBoundProof [UPPER BOUND(ID), 33 ms]
    (42) CpxRNTS
    (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (44) CpxRNTS
    (45) IntTrsBoundProof [UPPER BOUND(ID), 10.4 s]
    (46) CpxRNTS
    (47) IntTrsBoundProof [UPPER BOUND(ID), 4153 ms]
    (48) CpxRNTS
    (49) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (50) CpxRNTS
    (51) IntTrsBoundProof [UPPER BOUND(ID), 7176 ms]
    (52) CpxRNTS
    (53) IntTrsBoundProof [UPPER BOUND(ID), 3019 ms]
    (54) CpxRNTS
    (55) FinalProof [FINISHED, 0 ms]
    (56) BOUNDS(1, n^2)
(57) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 4 ms]
(58) TRS for Loop Detection
    (59) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
    (60) BEST
        (61) proven lower bound
            (62) LowerBoundPropagationProof [FINISHED, 0 ms]
            (63) BOUNDS(n^1, INF)
        (64) TRS for Loop Detection


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

(0)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   COND1(true, z0, z1, z2) -> c(COND2(gr(z1, z2), z0, z1, z2), GR(z1, z2))
   COND2(true, z0, z1, z2) -> c1(COND2(gr(z1, z2), z0, p(z1), z2), GR(z1, z2))
   COND2(true, z0, z1, z2) -> c2(COND2(gr(z1, z2), z0, p(z1), z2), P(z1))
   COND2(false, z0, z1, z2) -> c3(COND1(gr(z0, z2), p(z0), z1, z2), GR(z0, z2))
   COND2(false, z0, z1, z2) -> c4(COND1(gr(z0, z2), p(z0), z1, z2), 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

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

   cond1(true, z0, z1, z2) -> cond2(gr(z1, z2), z0, z1, z2)
   cond2(true, z0, z1, z2) -> cond2(gr(z1, z2), z0, p(z1), z2)
   cond2(false, z0, z1, z2) -> cond1(gr(z0, z2), p(z0), z1, z2)
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   p(0) -> 0
   p(s(z0)) -> z0

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

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

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


The TRS R consists of the following rules:

   COND1(true, z0, z1, z2) -> c(COND2(gr(z1, z2), z0, z1, z2), GR(z1, z2))
   COND2(true, z0, z1, z2) -> c1(COND2(gr(z1, z2), z0, p(z1), z2), GR(z1, z2))
   COND2(true, z0, z1, z2) -> c2(COND2(gr(z1, z2), z0, p(z1), z2), P(z1))
   COND2(false, z0, z1, z2) -> c3(COND1(gr(z0, z2), p(z0), z1, z2), GR(z0, z2))
   COND2(false, z0, z1, z2) -> c4(COND1(gr(z0, z2), p(z0), z1, z2), 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

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

   cond1(true, z0, z1, z2) -> cond2(gr(z1, z2), z0, z1, z2)
   cond2(true, z0, z1, z2) -> cond2(gr(z1, z2), z0, p(z1), z2)
   cond2(false, z0, z1, z2) -> cond1(gr(z0, z2), p(z0), z1, z2)
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   p(0) -> 0
   p(s(z0)) -> z0

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

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

(4)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2).


The TRS R consists of the following rules:

   COND1(true, z0, z1, z2) -> c(COND2(gr(z1, z2), z0, z1, z2), GR(z1, z2)) [1]
   COND2(true, z0, z1, z2) -> c1(COND2(gr(z1, z2), z0, p(z1), z2), GR(z1, z2)) [1]
   COND2(true, z0, z1, z2) -> c2(COND2(gr(z1, z2), z0, p(z1), z2), P(z1)) [1]
   COND2(false, z0, z1, z2) -> c3(COND1(gr(z0, z2), p(z0), z1, z2), GR(z0, z2)) [1]
   COND2(false, z0, z1, z2) -> c4(COND1(gr(z0, z2), p(z0), z1, z2), P(z0)) [1]
   GR(0, z0) -> c5 [1]
   GR(s(z0), 0) -> c6 [1]
   GR(s(z0), s(z1)) -> c7(GR(z0, z1)) [1]
   P(0) -> c8 [1]
   P(s(z0)) -> c9 [1]
   cond1(true, z0, z1, z2) -> cond2(gr(z1, z2), z0, z1, z2) [0]
   cond2(true, z0, z1, z2) -> cond2(gr(z1, z2), z0, p(z1), z2) [0]
   cond2(false, z0, z1, z2) -> cond1(gr(z0, z2), p(z0), z1, z2) [0]
   gr(0, z0) -> false [0]
   gr(s(z0), 0) -> true [0]
   gr(s(z0), s(z1)) -> gr(z0, z1) [0]
   p(0) -> 0 [0]
   p(s(z0)) -> z0 [0]

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

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

(6)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   COND1(true, z0, z1, z2) -> c(COND2(gr(z1, z2), z0, z1, z2), GR(z1, z2)) [1]
   COND2(true, z0, z1, z2) -> c1(COND2(gr(z1, z2), z0, p(z1), z2), GR(z1, z2)) [1]
   COND2(true, z0, z1, z2) -> c2(COND2(gr(z1, z2), z0, p(z1), z2), P(z1)) [1]
   COND2(false, z0, z1, z2) -> c3(COND1(gr(z0, z2), p(z0), z1, z2), GR(z0, z2)) [1]
   COND2(false, z0, z1, z2) -> c4(COND1(gr(z0, z2), p(z0), z1, z2), P(z0)) [1]
   GR(0, z0) -> c5 [1]
   GR(s(z0), 0) -> c6 [1]
   GR(s(z0), s(z1)) -> c7(GR(z0, z1)) [1]
   P(0) -> c8 [1]
   P(s(z0)) -> c9 [1]
   cond1(true, z0, z1, z2) -> cond2(gr(z1, z2), z0, z1, z2) [0]
   cond2(true, z0, z1, z2) -> cond2(gr(z1, z2), z0, p(z1), z2) [0]
   cond2(false, z0, z1, z2) -> cond1(gr(z0, z2), p(z0), z1, z2) [0]
   gr(0, z0) -> false [0]
   gr(s(z0), 0) -> true [0]
   gr(s(z0), s(z1)) -> gr(z0, z1) [0]
   p(0) -> 0 [0]
   p(s(z0)) -> z0 [0]

The TRS has the following type information:
COND1 :: true:false -> 0:s -> 0:s -> 0:s -> c
true :: true:false
c :: c1:c2:c3:c4 -> c5:c6:c7 -> c
COND2 :: true:false -> 0:s -> 0:s -> 0:s -> c1:c2:c3:c4
gr :: 0:s -> 0:s -> true:false
GR :: 0:s -> 0:s -> c5:c6:c7
c1 :: c1:c2:c3:c4 -> c5:c6:c7 -> c1:c2:c3:c4
p :: 0:s -> 0:s
c2 :: c1:c2:c3:c4 -> c8:c9 -> c1:c2:c3:c4
P :: 0:s -> c8:c9
false :: true:false
c3 :: c -> c5:c6:c7 -> c1:c2:c3:c4
c4 :: c -> c8:c9 -> c1:c2:c3:c4
0 :: 0:s
c5 :: c5:c6:c7
s :: 0:s -> 0:s
c6 :: c5:c6:c7
c7 :: c5:c6:c7 -> c5:c6:c7
c8 :: c8:c9
c9 :: c8:c9
cond1 :: true:false -> 0:s -> 0:s -> 0:s -> cond1:cond2
cond2 :: true:false -> 0:s -> 0:s -> 0:s -> cond1:cond2

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

(7) 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:

   COND1_4
   COND2_4
   GR_2
   P_1

(c) The following functions are completely defined:

   cond1_4
   cond2_4
   gr_2
   p_1

Due to the following rules being added:

   cond1(v0, v1, v2, v3) -> const2 [0]
   cond2(v0, v1, v2, v3) -> const2 [0]
   gr(v0, v1) -> null_gr [0]
   p(v0) -> 0 [0]

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

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

(8)
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:

   COND1(true, z0, z1, z2) -> c(COND2(gr(z1, z2), z0, z1, z2), GR(z1, z2)) [1]
   COND2(true, z0, z1, z2) -> c1(COND2(gr(z1, z2), z0, p(z1), z2), GR(z1, z2)) [1]
   COND2(true, z0, z1, z2) -> c2(COND2(gr(z1, z2), z0, p(z1), z2), P(z1)) [1]
   COND2(false, z0, z1, z2) -> c3(COND1(gr(z0, z2), p(z0), z1, z2), GR(z0, z2)) [1]
   COND2(false, z0, z1, z2) -> c4(COND1(gr(z0, z2), p(z0), z1, z2), P(z0)) [1]
   GR(0, z0) -> c5 [1]
   GR(s(z0), 0) -> c6 [1]
   GR(s(z0), s(z1)) -> c7(GR(z0, z1)) [1]
   P(0) -> c8 [1]
   P(s(z0)) -> c9 [1]
   cond1(true, z0, z1, z2) -> cond2(gr(z1, z2), z0, z1, z2) [0]
   cond2(true, z0, z1, z2) -> cond2(gr(z1, z2), z0, p(z1), z2) [0]
   cond2(false, z0, z1, z2) -> cond1(gr(z0, z2), p(z0), z1, z2) [0]
   gr(0, z0) -> false [0]
   gr(s(z0), 0) -> true [0]
   gr(s(z0), s(z1)) -> gr(z0, z1) [0]
   p(0) -> 0 [0]
   p(s(z0)) -> z0 [0]
   cond1(v0, v1, v2, v3) -> const2 [0]
   cond2(v0, v1, v2, v3) -> const2 [0]
   gr(v0, v1) -> null_gr [0]
   p(v0) -> 0 [0]

The TRS has the following type information:
COND1 :: true:false:null_gr -> 0:s -> 0:s -> 0:s -> c
true :: true:false:null_gr
c :: c1:c2:c3:c4 -> c5:c6:c7 -> c
COND2 :: true:false:null_gr -> 0:s -> 0:s -> 0:s -> c1:c2:c3:c4
gr :: 0:s -> 0:s -> true:false:null_gr
GR :: 0:s -> 0:s -> c5:c6:c7
c1 :: c1:c2:c3:c4 -> c5:c6:c7 -> c1:c2:c3:c4
p :: 0:s -> 0:s
c2 :: c1:c2:c3:c4 -> c8:c9 -> c1:c2:c3:c4
P :: 0:s -> c8:c9
false :: true:false:null_gr
c3 :: c -> c5:c6:c7 -> c1:c2:c3:c4
c4 :: c -> c8:c9 -> c1:c2:c3:c4
0 :: 0:s
c5 :: c5:c6:c7
s :: 0:s -> 0:s
c6 :: c5:c6:c7
c7 :: c5:c6:c7 -> c5:c6:c7
c8 :: c8:c9
c9 :: c8:c9
cond1 :: true:false:null_gr -> 0:s -> 0:s -> 0:s -> const2
cond2 :: true:false:null_gr -> 0:s -> 0:s -> 0:s -> const2
const2 :: const2
null_gr :: true:false:null_gr
const :: c
const1 :: c1:c2:c3:c4

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

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

(10)
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:

   COND1(true, z0, 0, z2) -> c(COND2(false, z0, 0, z2), GR(0, z2)) [1]
   COND1(true, z0, s(z0'), 0) -> c(COND2(true, z0, s(z0'), 0), GR(s(z0'), 0)) [1]
   COND1(true, z0, s(z0''), s(z1')) -> c(COND2(gr(z0'', z1'), z0, s(z0''), s(z1')), GR(s(z0''), s(z1'))) [1]
   COND1(true, z0, z1, z2) -> c(COND2(null_gr, z0, z1, z2), GR(z1, z2)) [1]
   COND2(true, z0, 0, z2) -> c1(COND2(false, z0, 0, z2), GR(0, z2)) [1]
   COND2(true, z0, 0, z2) -> c1(COND2(false, z0, 0, z2), GR(0, z2)) [1]
   COND2(true, z0, s(z01), 0) -> c1(COND2(true, z0, z01, 0), GR(s(z01), 0)) [1]
   COND2(true, z0, s(z01), 0) -> c1(COND2(true, z0, 0, 0), GR(s(z01), 0)) [1]
   COND2(true, z0, s(z02), s(z1'')) -> c1(COND2(gr(z02, z1''), z0, z02, s(z1'')), GR(s(z02), s(z1''))) [1]
   COND2(true, z0, s(z02), s(z1'')) -> c1(COND2(gr(z02, z1''), z0, 0, s(z1'')), GR(s(z02), s(z1''))) [1]
   COND2(true, z0, 0, z2) -> c1(COND2(null_gr, z0, 0, z2), GR(0, z2)) [1]
   COND2(true, z0, s(z03), z2) -> c1(COND2(null_gr, z0, z03, z2), GR(s(z03), z2)) [1]
   COND2(true, z0, z1, z2) -> c1(COND2(null_gr, z0, 0, z2), GR(z1, z2)) [1]
   COND2(true, z0, 0, z2) -> c2(COND2(false, z0, 0, z2), P(0)) [1]
   COND2(true, z0, 0, z2) -> c2(COND2(false, z0, 0, z2), P(0)) [1]
   COND2(true, z0, s(z04), 0) -> c2(COND2(true, z0, z04, 0), P(s(z04))) [1]
   COND2(true, z0, s(z04), 0) -> c2(COND2(true, z0, 0, 0), P(s(z04))) [1]
   COND2(true, z0, s(z05), s(z11)) -> c2(COND2(gr(z05, z11), z0, z05, s(z11)), P(s(z05))) [1]
   COND2(true, z0, s(z05), s(z11)) -> c2(COND2(gr(z05, z11), z0, 0, s(z11)), P(s(z05))) [1]
   COND2(true, z0, 0, z2) -> c2(COND2(null_gr, z0, 0, z2), P(0)) [1]
   COND2(true, z0, s(z06), z2) -> c2(COND2(null_gr, z0, z06, z2), P(s(z06))) [1]
   COND2(true, z0, z1, z2) -> c2(COND2(null_gr, z0, 0, z2), P(z1)) [1]
   COND2(false, 0, z1, z2) -> c3(COND1(false, 0, z1, z2), GR(0, z2)) [1]
   COND2(false, 0, z1, z2) -> c3(COND1(false, 0, z1, z2), GR(0, z2)) [1]
   COND2(false, s(z07), z1, 0) -> c3(COND1(true, z07, z1, 0), GR(s(z07), 0)) [1]
   COND2(false, s(z07), z1, 0) -> c3(COND1(true, 0, z1, 0), GR(s(z07), 0)) [1]
   COND2(false, s(z08), z1, s(z12)) -> c3(COND1(gr(z08, z12), z08, z1, s(z12)), GR(s(z08), s(z12))) [1]
   COND2(false, s(z08), z1, s(z12)) -> c3(COND1(gr(z08, z12), 0, z1, s(z12)), GR(s(z08), s(z12))) [1]
   COND2(false, 0, z1, z2) -> c3(COND1(null_gr, 0, z1, z2), GR(0, z2)) [1]
   COND2(false, s(z09), z1, z2) -> c3(COND1(null_gr, z09, z1, z2), GR(s(z09), z2)) [1]
   COND2(false, z0, z1, z2) -> c3(COND1(null_gr, 0, z1, z2), GR(z0, z2)) [1]
   COND2(false, 0, z1, z2) -> c4(COND1(false, 0, z1, z2), P(0)) [1]
   COND2(false, 0, z1, z2) -> c4(COND1(false, 0, z1, z2), P(0)) [1]
   COND2(false, s(z010), z1, 0) -> c4(COND1(true, z010, z1, 0), P(s(z010))) [1]
   COND2(false, s(z010), z1, 0) -> c4(COND1(true, 0, z1, 0), P(s(z010))) [1]
   COND2(false, s(z011), z1, s(z13)) -> c4(COND1(gr(z011, z13), z011, z1, s(z13)), P(s(z011))) [1]
   COND2(false, s(z011), z1, s(z13)) -> c4(COND1(gr(z011, z13), 0, z1, s(z13)), P(s(z011))) [1]
   COND2(false, 0, z1, z2) -> c4(COND1(null_gr, 0, z1, z2), P(0)) [1]
   COND2(false, s(z012), z1, z2) -> c4(COND1(null_gr, z012, z1, z2), P(s(z012))) [1]
   COND2(false, z0, z1, z2) -> c4(COND1(null_gr, 0, z1, z2), P(z0)) [1]
   GR(0, z0) -> c5 [1]
   GR(s(z0), 0) -> c6 [1]
   GR(s(z0), s(z1)) -> c7(GR(z0, z1)) [1]
   P(0) -> c8 [1]
   P(s(z0)) -> c9 [1]
   cond1(true, z0, 0, z2) -> cond2(false, z0, 0, z2) [0]
   cond1(true, z0, s(z013), 0) -> cond2(true, z0, s(z013), 0) [0]
   cond1(true, z0, s(z014), s(z14)) -> cond2(gr(z014, z14), z0, s(z014), s(z14)) [0]
   cond1(true, z0, z1, z2) -> cond2(null_gr, z0, z1, z2) [0]
   cond2(true, z0, 0, z2) -> cond2(false, z0, 0, z2) [0]
   cond2(true, z0, 0, z2) -> cond2(false, z0, 0, z2) [0]
   cond2(true, z0, s(z015), 0) -> cond2(true, z0, z015, 0) [0]
   cond2(true, z0, s(z015), 0) -> cond2(true, z0, 0, 0) [0]
   cond2(true, z0, s(z016), s(z15)) -> cond2(gr(z016, z15), z0, z016, s(z15)) [0]
   cond2(true, z0, s(z016), s(z15)) -> cond2(gr(z016, z15), z0, 0, s(z15)) [0]
   cond2(true, z0, 0, z2) -> cond2(null_gr, z0, 0, z2) [0]
   cond2(true, z0, s(z017), z2) -> cond2(null_gr, z0, z017, z2) [0]
   cond2(true, z0, z1, z2) -> cond2(null_gr, z0, 0, z2) [0]
   cond2(false, 0, z1, z2) -> cond1(false, 0, z1, z2) [0]
   cond2(false, 0, z1, z2) -> cond1(false, 0, z1, z2) [0]
   cond2(false, s(z018), z1, 0) -> cond1(true, z018, z1, 0) [0]
   cond2(false, s(z018), z1, 0) -> cond1(true, 0, z1, 0) [0]
   cond2(false, s(z019), z1, s(z16)) -> cond1(gr(z019, z16), z019, z1, s(z16)) [0]
   cond2(false, s(z019), z1, s(z16)) -> cond1(gr(z019, z16), 0, z1, s(z16)) [0]
   cond2(false, 0, z1, z2) -> cond1(null_gr, 0, z1, z2) [0]
   cond2(false, s(z020), z1, z2) -> cond1(null_gr, z020, z1, z2) [0]
   cond2(false, z0, z1, z2) -> cond1(null_gr, 0, z1, z2) [0]
   gr(0, z0) -> false [0]
   gr(s(z0), 0) -> true [0]
   gr(s(z0), s(z1)) -> gr(z0, z1) [0]
   p(0) -> 0 [0]
   p(s(z0)) -> z0 [0]
   cond1(v0, v1, v2, v3) -> const2 [0]
   cond2(v0, v1, v2, v3) -> const2 [0]
   gr(v0, v1) -> null_gr [0]
   p(v0) -> 0 [0]

The TRS has the following type information:
COND1 :: true:false:null_gr -> 0:s -> 0:s -> 0:s -> c
true :: true:false:null_gr
c :: c1:c2:c3:c4 -> c5:c6:c7 -> c
COND2 :: true:false:null_gr -> 0:s -> 0:s -> 0:s -> c1:c2:c3:c4
gr :: 0:s -> 0:s -> true:false:null_gr
GR :: 0:s -> 0:s -> c5:c6:c7
c1 :: c1:c2:c3:c4 -> c5:c6:c7 -> c1:c2:c3:c4
p :: 0:s -> 0:s
c2 :: c1:c2:c3:c4 -> c8:c9 -> c1:c2:c3:c4
P :: 0:s -> c8:c9
false :: true:false:null_gr
c3 :: c -> c5:c6:c7 -> c1:c2:c3:c4
c4 :: c -> c8:c9 -> c1:c2:c3:c4
0 :: 0:s
c5 :: c5:c6:c7
s :: 0:s -> 0:s
c6 :: c5:c6:c7
c7 :: c5:c6:c7 -> c5:c6:c7
c8 :: c8:c9
c9 :: c8:c9
cond1 :: true:false:null_gr -> 0:s -> 0:s -> 0:s -> const2
cond2 :: true:false:null_gr -> 0:s -> 0:s -> 0:s -> const2
const2 :: const2
null_gr :: true:false:null_gr
const :: c
const1 :: c1:c2:c3:c4

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

(11) 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
   false => 1
   0 => 0
   c5 => 0
   c6 => 1
   c8 => 0
   c9 => 1
   const2 => 0
   null_gr => 0
   const => 0
   const1 => 0

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

(12)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z0'', z1'), z0, 1 + z0'', 1 + z1') + GR(1 + z0'', 1 + z1') :|: z = 2, z'' = 1 + z0'', z3 = 1 + z1', z1' >= 0, z0 >= 0, z0'' >= 0, z' = z0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z0, 1 + z0', 0) + GR(1 + z0', 0) :|: z = 2, z0' >= 0, z3 = 0, z0 >= 0, z'' = 1 + z0', z' = z0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z0, 0, z2) + GR(0, z2) :|: z = 2, z'' = 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z0, z1, z2) + GR(z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z02, z1''), z0, z02, 1 + z1'') + GR(1 + z02, 1 + z1'') :|: z = 2, z02 >= 0, z0 >= 0, z3 = 1 + z1'', z' = z0, z'' = 1 + z02, z1'' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z02, z1''), z0, 0, 1 + z1'') + GR(1 + z02, 1 + z1'') :|: z = 2, z02 >= 0, z0 >= 0, z3 = 1 + z1'', z' = z0, z'' = 1 + z02, z1'' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z05, z11), z0, z05, 1 + z11) + P(1 + z05) :|: z = 2, z3 = 1 + z11, z11 >= 0, z'' = 1 + z05, z0 >= 0, z05 >= 0, z' = z0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z05, z11), z0, 0, 1 + z11) + P(1 + z05) :|: z = 2, z3 = 1 + z11, z11 >= 0, z'' = 1 + z05, z0 >= 0, z05 >= 0, z' = z0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z0, z01, 0) + GR(1 + z01, 0) :|: z = 2, z01 >= 0, z3 = 0, z0 >= 0, z' = z0, z'' = 1 + z01
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z0, z04, 0) + P(1 + z04) :|: z = 2, z'' = 1 + z04, z04 >= 0, z3 = 0, z0 >= 0, z' = z0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z0, 0, 0) + P(1 + z04) :|: z = 2, z'' = 1 + z04, z04 >= 0, z3 = 0, z0 >= 0, z' = z0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z0, 0, 0) + GR(1 + z01, 0) :|: z = 2, z01 >= 0, z3 = 0, z0 >= 0, z' = z0, z'' = 1 + z01
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z0, 0, z2) + P(0) :|: z = 2, z'' = 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z0, 0, z2) + GR(0, z2) :|: z = 2, z'' = 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z0, z03, z2) + GR(1 + z03, z2) :|: z = 2, z'' = 1 + z03, z0 >= 0, z03 >= 0, z3 = z2, z' = z0, z2 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z0, z06, z2) + P(1 + z06) :|: z = 2, z'' = 1 + z06, z06 >= 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z0, 0, z2) + P(z1) :|: z = 2, z1 >= 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z0, 0, z2) + P(0) :|: z = 2, z'' = 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z0, 0, z2) + GR(z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z0, 0, z2) + GR(0, z2) :|: z = 2, z'' = 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z011, z13), z011, z1, 1 + z13) + P(1 + z011) :|: z3 = 1 + z13, z011 >= 0, z1 >= 0, z = 1, z' = 1 + z011, z13 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z011, z13), 0, z1, 1 + z13) + P(1 + z011) :|: z3 = 1 + z13, z011 >= 0, z1 >= 0, z = 1, z' = 1 + z011, z13 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z08, z12), z08, z1, 1 + z12) + GR(1 + z08, 1 + z12) :|: z08 >= 0, z3 = 1 + z12, z1 >= 0, z' = 1 + z08, z = 1, z12 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z08, z12), 0, z1, 1 + z12) + GR(1 + z08, 1 + z12) :|: z08 >= 0, z3 = 1 + z12, z1 >= 0, z' = 1 + z08, z = 1, z12 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, z010, z1, 0) + P(1 + z010) :|: z1 >= 0, z = 1, z3 = 0, z' = 1 + z010, z010 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, z07, z1, 0) + GR(1 + z07, 0) :|: z1 >= 0, z07 >= 0, z = 1, z3 = 0, z' = 1 + z07, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, 0, z1, 0) + P(1 + z010) :|: z1 >= 0, z = 1, z3 = 0, z' = 1 + z010, z010 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, 0, z1, 0) + GR(1 + z07, 0) :|: z1 >= 0, z07 >= 0, z = 1, z3 = 0, z' = 1 + z07, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(1, 0, z1, z2) + P(0) :|: z1 >= 0, z = 1, z3 = z2, z2 >= 0, z' = 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(1, 0, z1, z2) + GR(0, z2) :|: z1 >= 0, z = 1, z3 = z2, z2 >= 0, z' = 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, z012, z1, z2) + P(1 + z012) :|: z1 >= 0, z = 1, z' = 1 + z012, z012 >= 0, z3 = z2, z2 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, z09, z1, z2) + GR(1 + z09, z2) :|: z1 >= 0, z = 1, z' = 1 + z09, z09 >= 0, z3 = z2, z2 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z1, z2) + P(z0) :|: z1 >= 0, z = 1, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z1, z2) + P(0) :|: z1 >= 0, z = 1, z3 = z2, z2 >= 0, z' = 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z1, z2) + GR(z0, z2) :|: z1 >= 0, z = 1, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z1, z2) + GR(0, z2) :|: z1 >= 0, z = 1, z3 = z2, z2 >= 0, z' = 0, z'' = z1
   GR(z, z') -{ 1 }-> 1 :|: z = 1 + z0, z0 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z0 >= 0, z = 0, z' = z0
   GR(z, z') -{ 1 }-> 1 + GR(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   P(z) -{ 1 }-> 1 :|: z = 1 + z0, z0 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(gr(z014, z14), z0, 1 + z014, 1 + z14) :|: z = 2, z'' = 1 + z014, z3 = 1 + z14, z014 >= 0, z0 >= 0, z' = z0, z14 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z0, 1 + z013, 0) :|: z = 2, z'' = 1 + z013, z3 = 0, z013 >= 0, z0 >= 0, z' = z0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z0, 0, z2) :|: z = 2, z'' = 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z3 = v3, v2 >= 0, v3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z016, z15), z0, z016, 1 + z15) :|: z = 2, z15 >= 0, z'' = 1 + z016, z0 >= 0, z016 >= 0, z3 = 1 + z15, z' = z0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z016, z15), z0, 0, 1 + z15) :|: z = 2, z15 >= 0, z'' = 1 + z016, z0 >= 0, z016 >= 0, z3 = 1 + z15, z' = z0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z0, z015, 0) :|: z = 2, z'' = 1 + z015, z015 >= 0, z3 = 0, z0 >= 0, z' = z0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z0, 0, 0) :|: z = 2, z'' = 1 + z015, z015 >= 0, z3 = 0, z0 >= 0, z' = z0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z0, 0, z2) :|: z = 2, z'' = 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z0, z017, z2) :|: z = 2, z'' = 1 + z017, z0 >= 0, z3 = z2, z' = z0, z017 >= 0, z2 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z0, 0, z2) :|: z = 2, z'' = 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z0, 0, z2) :|: z = 2, z1 >= 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z019, z16), z019, z1, 1 + z16) :|: z019 >= 0, z1 >= 0, z = 1, z16 >= 0, z' = 1 + z019, z3 = 1 + z16, z'' = z1
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z019, z16), 0, z1, 1 + z16) :|: z019 >= 0, z1 >= 0, z = 1, z16 >= 0, z' = 1 + z019, z3 = 1 + z16, z'' = z1
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z018, z1, 0) :|: z1 >= 0, z = 1, z3 = 0, z' = 1 + z018, z018 >= 0, z'' = z1
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z1, 0) :|: z1 >= 0, z = 1, z3 = 0, z' = 1 + z018, z018 >= 0, z'' = z1
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z1, z2) :|: z1 >= 0, z = 1, z3 = z2, z2 >= 0, z' = 0, z'' = z1
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z020, z1, z2) :|: z1 >= 0, z = 1, z' = 1 + z020, z020 >= 0, z3 = z2, z2 >= 0, z'' = z1
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z1, z2) :|: z1 >= 0, z = 1, z3 = z2, z2 >= 0, z' = 0, z'' = z1
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z1, z2) :|: z1 >= 0, z = 1, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z3 = v3, v2 >= 0, v3 >= 0
   gr(z, z') -{ 0 }-> 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


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

(13) InliningProof (UPPER BOUND(ID))
Inlined the following terminating rules on right-hand sides where appropriate:

   P(z) -{ 1 }-> 1 :|: z = 1 + z0, z0 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0

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

(14)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z0'', z1'), z0, 1 + z0'', 1 + z1') + GR(1 + z0'', 1 + z1') :|: z = 2, z'' = 1 + z0'', z3 = 1 + z1', z1' >= 0, z0 >= 0, z0'' >= 0, z' = z0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z0, 1 + z0', 0) + GR(1 + z0', 0) :|: z = 2, z0' >= 0, z3 = 0, z0 >= 0, z'' = 1 + z0', z' = z0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z0, 0, z2) + GR(0, z2) :|: z = 2, z'' = 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z0, z1, z2) + GR(z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z02, z1''), z0, z02, 1 + z1'') + GR(1 + z02, 1 + z1'') :|: z = 2, z02 >= 0, z0 >= 0, z3 = 1 + z1'', z' = z0, z'' = 1 + z02, z1'' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z02, z1''), z0, 0, 1 + z1'') + GR(1 + z02, 1 + z1'') :|: z = 2, z02 >= 0, z0 >= 0, z3 = 1 + z1'', z' = z0, z'' = 1 + z02, z1'' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z05, z11), z0, z05, 1 + z11) + 1 :|: z = 2, z3 = 1 + z11, z11 >= 0, z'' = 1 + z05, z0 >= 0, z05 >= 0, z' = z0, 1 + z05 = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z05, z11), z0, 0, 1 + z11) + 1 :|: z = 2, z3 = 1 + z11, z11 >= 0, z'' = 1 + z05, z0 >= 0, z05 >= 0, z' = z0, 1 + z05 = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z0, z01, 0) + GR(1 + z01, 0) :|: z = 2, z01 >= 0, z3 = 0, z0 >= 0, z' = z0, z'' = 1 + z01
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z0, z04, 0) + 1 :|: z = 2, z'' = 1 + z04, z04 >= 0, z3 = 0, z0 >= 0, z' = z0, 1 + z04 = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z0, 0, 0) + GR(1 + z01, 0) :|: z = 2, z01 >= 0, z3 = 0, z0 >= 0, z' = z0, z'' = 1 + z01
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z0, 0, 0) + 1 :|: z = 2, z'' = 1 + z04, z04 >= 0, z3 = 0, z0 >= 0, z' = z0, 1 + z04 = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z0, 0, z2) + GR(0, z2) :|: z = 2, z'' = 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(1, z0, 0, z2) + 0 :|: z = 2, z'' = 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z0, z03, z2) + GR(1 + z03, z2) :|: z = 2, z'' = 1 + z03, z0 >= 0, z03 >= 0, z3 = z2, z' = z0, z2 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z0, z06, z2) + 1 :|: z = 2, z'' = 1 + z06, z06 >= 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, 1 + z06 = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z0, 0, z2) + GR(z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z0, 0, z2) + GR(0, z2) :|: z = 2, z'' = 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z0, 0, z2) + 1 :|: z = 2, z1 >= 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1, z1 = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z0, 0, z2) + 0 :|: z = 2, z'' = 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z0, 0, z2) + 0 :|: z = 2, z1 >= 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1, z1 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z011, z13), z011, z1, 1 + z13) + 1 :|: z3 = 1 + z13, z011 >= 0, z1 >= 0, z = 1, z' = 1 + z011, z13 >= 0, z'' = z1, 1 + z011 = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z011, z13), 0, z1, 1 + z13) + 1 :|: z3 = 1 + z13, z011 >= 0, z1 >= 0, z = 1, z' = 1 + z011, z13 >= 0, z'' = z1, 1 + z011 = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z08, z12), z08, z1, 1 + z12) + GR(1 + z08, 1 + z12) :|: z08 >= 0, z3 = 1 + z12, z1 >= 0, z' = 1 + z08, z = 1, z12 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z08, z12), 0, z1, 1 + z12) + GR(1 + z08, 1 + z12) :|: z08 >= 0, z3 = 1 + z12, z1 >= 0, z' = 1 + z08, z = 1, z12 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, z010, z1, 0) + 1 :|: z1 >= 0, z = 1, z3 = 0, z' = 1 + z010, z010 >= 0, z'' = z1, 1 + z010 = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, z07, z1, 0) + GR(1 + z07, 0) :|: z1 >= 0, z07 >= 0, z = 1, z3 = 0, z' = 1 + z07, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, 0, z1, 0) + GR(1 + z07, 0) :|: z1 >= 0, z07 >= 0, z = 1, z3 = 0, z' = 1 + z07, z'' = z1
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, 0, z1, 0) + 1 :|: z1 >= 0, z = 1, z3 = 0, z' = 1 + z010, z010 >= 0, z'' = z1, 1 + z010 = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(1, 0, z1, z2) + GR(0, z2) :|: z1 >= 0, z = 1, z3 = z2, z2 >= 0, z' = 0, z'' = z1
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(1, 0, z1, z2) + 0 :|: z1 >= 0, z = 1, z3 = z2, z2 >= 0, z' = 0, z'' = z1, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, z012, z1, z2) + 1 :|: z1 >= 0, z = 1, z' = 1 + z012, z012 >= 0, z3 = z2, z2 >= 0, z'' = z1, 1 + z012 = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, z09, z1, z2) + GR(1 + z09, z2) :|: z1 >= 0, z = 1, z' = 1 + z09, z09 >= 0, z3 = z2, z2 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z1, z2) + GR(z0, z2) :|: z1 >= 0, z = 1, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z1, z2) + GR(0, z2) :|: z1 >= 0, z = 1, z3 = z2, z2 >= 0, z' = 0, z'' = z1
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z1, z2) + 1 :|: z1 >= 0, z = 1, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1, z0 = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z1, z2) + 0 :|: z1 >= 0, z = 1, z3 = z2, z2 >= 0, z' = 0, z'' = z1, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z1, z2) + 0 :|: z1 >= 0, z = 1, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1, z0 = 0
   GR(z, z') -{ 1 }-> 1 :|: z = 1 + z0, z0 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z0 >= 0, z = 0, z' = z0
   GR(z, z') -{ 1 }-> 1 + GR(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   P(z) -{ 1 }-> 1 :|: z = 1 + z0, z0 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(gr(z014, z14), z0, 1 + z014, 1 + z14) :|: z = 2, z'' = 1 + z014, z3 = 1 + z14, z014 >= 0, z0 >= 0, z' = z0, z14 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z0, 1 + z013, 0) :|: z = 2, z'' = 1 + z013, z3 = 0, z013 >= 0, z0 >= 0, z' = z0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z0, 0, z2) :|: z = 2, z'' = 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z3 = v3, v2 >= 0, v3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z016, z15), z0, z016, 1 + z15) :|: z = 2, z15 >= 0, z'' = 1 + z016, z0 >= 0, z016 >= 0, z3 = 1 + z15, z' = z0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z016, z15), z0, 0, 1 + z15) :|: z = 2, z15 >= 0, z'' = 1 + z016, z0 >= 0, z016 >= 0, z3 = 1 + z15, z' = z0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z0, z015, 0) :|: z = 2, z'' = 1 + z015, z015 >= 0, z3 = 0, z0 >= 0, z' = z0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z0, 0, 0) :|: z = 2, z'' = 1 + z015, z015 >= 0, z3 = 0, z0 >= 0, z' = z0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z0, 0, z2) :|: z = 2, z'' = 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z0, z017, z2) :|: z = 2, z'' = 1 + z017, z0 >= 0, z3 = z2, z' = z0, z017 >= 0, z2 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z0, 0, z2) :|: z = 2, z'' = 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z0, 0, z2) :|: z = 2, z1 >= 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z019, z16), z019, z1, 1 + z16) :|: z019 >= 0, z1 >= 0, z = 1, z16 >= 0, z' = 1 + z019, z3 = 1 + z16, z'' = z1
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z019, z16), 0, z1, 1 + z16) :|: z019 >= 0, z1 >= 0, z = 1, z16 >= 0, z' = 1 + z019, z3 = 1 + z16, z'' = z1
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z018, z1, 0) :|: z1 >= 0, z = 1, z3 = 0, z' = 1 + z018, z018 >= 0, z'' = z1
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z1, 0) :|: z1 >= 0, z = 1, z3 = 0, z' = 1 + z018, z018 >= 0, z'' = z1
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z1, z2) :|: z1 >= 0, z = 1, z3 = z2, z2 >= 0, z' = 0, z'' = z1
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z020, z1, z2) :|: z1 >= 0, z = 1, z' = 1 + z020, z020 >= 0, z3 = z2, z2 >= 0, z'' = z1
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z1, z2) :|: z1 >= 0, z = 1, z3 = z2, z2 >= 0, z' = 0, z'' = z1
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z1, z2) :|: z1 >= 0, z = 1, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z3 = v3, v2 >= 0, v3 >= 0
   gr(z, z') -{ 0 }-> 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


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(15) SimplificationProof (BOTH BOUNDS(ID, ID))
Simplified the RNTS by moving equalities from the constraints into the right-hand sides.
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(16)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', 1 + (z'' - 1), 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', z'', z3) + GR(z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', 0, 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', 0, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', z'' - 1, 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', z'' - 1, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(1, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', 0, z3) + GR(z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 1 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', z'' - 1, z3) + GR(1 + (z'' - 1), z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', z'' - 1, z3) + 1 :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + GR(1 + (z' - 1), 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + GR(1 + (z' - 1), 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, 0, z'', 0) + GR(1 + (z' - 1), 0) :|: z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, 0, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, z' - 1, z'', 0) + GR(1 + (z' - 1), 0) :|: z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, z' - 1, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(1, 0, z'', z3) + GR(0, z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(1, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z'', z3) + GR(z', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z'', z3) + GR(0, z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 1 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, z' - 1, z'', z3) + GR(1 + (z' - 1), z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, z' - 1, z'', z3) + 1 :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> 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


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

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

   { P }
   { GR }
   { gr }
   { p }
   { COND2, COND1 }
   { cond2, cond1 }

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

(18)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', 1 + (z'' - 1), 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', z'', z3) + GR(z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', 0, 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', 0, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', z'' - 1, 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', z'' - 1, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(1, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', 0, z3) + GR(z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 1 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', z'' - 1, z3) + GR(1 + (z'' - 1), z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', z'' - 1, z3) + 1 :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + GR(1 + (z' - 1), 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + GR(1 + (z' - 1), 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, 0, z'', 0) + GR(1 + (z' - 1), 0) :|: z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, 0, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, z' - 1, z'', 0) + GR(1 + (z' - 1), 0) :|: z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, z' - 1, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(1, 0, z'', z3) + GR(0, z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(1, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z'', z3) + GR(z', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z'', z3) + GR(0, z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 1 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, z' - 1, z'', z3) + GR(1 + (z' - 1), z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, z' - 1, z'', z3) + 1 :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> 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: {P}, {GR}, {gr}, {p}, {COND2,COND1}, {cond2,cond1}

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

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

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

   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', 1 + (z'' - 1), 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', z'', z3) + GR(z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', 0, 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', 0, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', z'' - 1, 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', z'' - 1, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(1, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', 0, z3) + GR(z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 1 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', z'' - 1, z3) + GR(1 + (z'' - 1), z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', z'' - 1, z3) + 1 :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + GR(1 + (z' - 1), 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + GR(1 + (z' - 1), 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, 0, z'', 0) + GR(1 + (z' - 1), 0) :|: z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, 0, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, z' - 1, z'', 0) + GR(1 + (z' - 1), 0) :|: z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, z' - 1, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(1, 0, z'', z3) + GR(0, z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(1, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z'', z3) + GR(z', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z'', z3) + GR(0, z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 1 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, z' - 1, z'', z3) + GR(1 + (z' - 1), z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, z' - 1, z'', z3) + 1 :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> 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: {P}, {GR}, {gr}, {p}, {COND2,COND1}, {cond2,cond1}

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

(21) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', 1 + (z'' - 1), 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', z'', z3) + GR(z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', 0, 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', 0, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', z'' - 1, 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', z'' - 1, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(1, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', 0, z3) + GR(z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 1 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', z'' - 1, z3) + GR(1 + (z'' - 1), z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', z'' - 1, z3) + 1 :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + GR(1 + (z' - 1), 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + GR(1 + (z' - 1), 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, 0, z'', 0) + GR(1 + (z' - 1), 0) :|: z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, 0, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, z' - 1, z'', 0) + GR(1 + (z' - 1), 0) :|: z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, z' - 1, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(1, 0, z'', z3) + GR(0, z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(1, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z'', z3) + GR(z', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z'', z3) + GR(0, z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 1 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, z' - 1, z'', z3) + GR(1 + (z' - 1), z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, z' - 1, z'', z3) + 1 :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> 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: {P}, {GR}, {gr}, {p}, {COND2,COND1}, {cond2,cond1}
Previous analysis results are:
  P: runtime: ?, size: O(1) [1]

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

(23) 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: 1

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

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

   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', 1 + (z'' - 1), 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', z'', z3) + GR(z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', 0, 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', 0, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', z'' - 1, 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', z'' - 1, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(1, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', 0, z3) + GR(z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 1 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', z'' - 1, z3) + GR(1 + (z'' - 1), z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', z'' - 1, z3) + 1 :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + GR(1 + (z' - 1), 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + GR(1 + (z' - 1), 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, 0, z'', 0) + GR(1 + (z' - 1), 0) :|: z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, 0, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, z' - 1, z'', 0) + GR(1 + (z' - 1), 0) :|: z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, z' - 1, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(1, 0, z'', z3) + GR(0, z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(1, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z'', z3) + GR(z', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z'', z3) + GR(0, z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 1 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, z' - 1, z'', z3) + GR(1 + (z' - 1), z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, z' - 1, z'', z3) + 1 :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> 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}, {gr}, {p}, {COND2,COND1}, {cond2,cond1}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]

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(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'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', 1 + (z'' - 1), 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', z'', z3) + GR(z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', 0, 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', 0, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', z'' - 1, 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', z'' - 1, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(1, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', 0, z3) + GR(z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 1 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', z'' - 1, z3) + GR(1 + (z'' - 1), z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', z'' - 1, z3) + 1 :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + GR(1 + (z' - 1), 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + GR(1 + (z' - 1), 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, 0, z'', 0) + GR(1 + (z' - 1), 0) :|: z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, 0, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, z' - 1, z'', 0) + GR(1 + (z' - 1), 0) :|: z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, z' - 1, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(1, 0, z'', z3) + GR(0, z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(1, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z'', z3) + GR(z', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z'', z3) + GR(0, z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 1 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, z' - 1, z'', z3) + GR(1 + (z' - 1), z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, z' - 1, z'', z3) + 1 :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> 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}, {gr}, {p}, {COND2,COND1}, {cond2,cond1}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]

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

(27) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', 1 + (z'' - 1), 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', z'', z3) + GR(z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', 0, 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', 0, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', z'' - 1, 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', z'' - 1, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(1, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', 0, z3) + GR(z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 1 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', z'' - 1, z3) + GR(1 + (z'' - 1), z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', z'' - 1, z3) + 1 :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + GR(1 + (z' - 1), 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + GR(1 + (z' - 1), 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, 0, z'', 0) + GR(1 + (z' - 1), 0) :|: z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, 0, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, z' - 1, z'', 0) + GR(1 + (z' - 1), 0) :|: z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, z' - 1, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(1, 0, z'', z3) + GR(0, z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(1, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z'', z3) + GR(z', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z'', z3) + GR(0, z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 1 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, z' - 1, z'', z3) + GR(1 + (z' - 1), z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, z' - 1, z'', z3) + 1 :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> 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}, {gr}, {p}, {COND2,COND1}, {cond2,cond1}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: ?, size: O(n^1) [z]

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

(29) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', 1 + (z'' - 1), 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', z'', z3) + GR(z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + GR(1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', 0, 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', 0, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(2, z', z'' - 1, 0) + GR(1 + (z'' - 1), 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', z'' - 1, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(1, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(1, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', 0, z3) + GR(z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', 0, z3) + GR(0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 1 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND2(0, z', z'' - 1, z3) + GR(1 + (z'' - 1), z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', z'' - 1, z3) + 1 :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + GR(1 + (z' - 1), 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + GR(1 + (z' - 1), 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, 0, z'', 0) + GR(1 + (z' - 1), 0) :|: z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, 0, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(2, z' - 1, z'', 0) + GR(1 + (z' - 1), 0) :|: z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, z' - 1, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(1, 0, z'', z3) + GR(0, z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(1, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z'', z3) + GR(z', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, 0, z'', z3) + GR(0, z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 1 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 1 }-> 1 + COND1(0, z' - 1, z'', z3) + GR(1 + (z' - 1), z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, z' - 1, z'', z3) + 1 :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> 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}, {p}, {COND2,COND1}, {cond2,cond1}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]

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

(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'', z3) -{ 3 + z3 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) + s'' :|: s'' >= 0, s'' <= 1 + (z'' - 1), z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', 1 + (z'' - 1), 0) + s' :|: s' >= 0, s' <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(1, z', 0, z3) + s :|: s >= 0, s <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', z'', z3) + s1 :|: s1 >= 0, s1 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + s6 :|: s6 >= 0, s6 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + s5 :|: s5 >= 0, s5 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', 0, 0) + s4 :|: s4 >= 0, s4 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', 0, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', z'' - 1, 0) + s3 :|: s3 >= 0, s3 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', z'' - 1, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(1, z', 0, z3) + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(1, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', 0, z3) + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', 0, z3) + s9 :|: s9 >= 0, s9 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 1 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', z'' - 1, z3) + s8 :|: s8 >= 0, s8 <= 1 + (z'' - 1), z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', z'' - 1, z3) + 1 :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + s14 :|: s14 >= 0, s14 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + s13 :|: s13 >= 0, s13 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND1(2, 0, z'', 0) + s12 :|: s12 >= 0, s12 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, 0, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND1(2, z' - 1, z'', 0) + s11 :|: s11 >= 0, s11 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, z' - 1, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(1, 0, z'', z3) + s10 :|: s10 >= 0, s10 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(1, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, 0, z'', z3) + s15 :|: s15 >= 0, s15 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, 0, z'', z3) + s17 :|: s17 >= 0, s17 <= z', z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 1 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, z' - 1, z'', z3) + s16 :|: s16 >= 0, s16 <= 1 + (z' - 1), z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, z' - 1, z'', z3) + 1 :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s18 :|: s18 >= 0, s18 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> 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}, {p}, {COND2,COND1}, {cond2,cond1}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]

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

(33) 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

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

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

   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) + s'' :|: s'' >= 0, s'' <= 1 + (z'' - 1), z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', 1 + (z'' - 1), 0) + s' :|: s' >= 0, s' <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(1, z', 0, z3) + s :|: s >= 0, s <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', z'', z3) + s1 :|: s1 >= 0, s1 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + s6 :|: s6 >= 0, s6 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + s5 :|: s5 >= 0, s5 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', 0, 0) + s4 :|: s4 >= 0, s4 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', 0, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', z'' - 1, 0) + s3 :|: s3 >= 0, s3 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', z'' - 1, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(1, z', 0, z3) + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(1, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', 0, z3) + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', 0, z3) + s9 :|: s9 >= 0, s9 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 1 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', z'' - 1, z3) + s8 :|: s8 >= 0, s8 <= 1 + (z'' - 1), z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', z'' - 1, z3) + 1 :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + s14 :|: s14 >= 0, s14 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + s13 :|: s13 >= 0, s13 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND1(2, 0, z'', 0) + s12 :|: s12 >= 0, s12 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, 0, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND1(2, z' - 1, z'', 0) + s11 :|: s11 >= 0, s11 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, z' - 1, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(1, 0, z'', z3) + s10 :|: s10 >= 0, s10 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(1, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, 0, z'', z3) + s15 :|: s15 >= 0, s15 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, 0, z'', z3) + s17 :|: s17 >= 0, s17 <= z', z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 1 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, z' - 1, z'', z3) + s16 :|: s16 >= 0, s16 <= 1 + (z' - 1), z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, z' - 1, z'', z3) + 1 :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s18 :|: s18 >= 0, s18 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> 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}, {p}, {COND2,COND1}, {cond2,cond1}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  gr: runtime: ?, size: O(1) [2]

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

(35) 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

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

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

   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) + s'' :|: s'' >= 0, s'' <= 1 + (z'' - 1), z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', 1 + (z'' - 1), 0) + s' :|: s' >= 0, s' <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(1, z', 0, z3) + s :|: s >= 0, s <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', z'', z3) + s1 :|: s1 >= 0, s1 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + s6 :|: s6 >= 0, s6 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + s5 :|: s5 >= 0, s5 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) + 1 :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', 0, 0) + s4 :|: s4 >= 0, s4 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', 0, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', z'' - 1, 0) + s3 :|: s3 >= 0, s3 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', z'' - 1, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(1, z', 0, z3) + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(1, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', 0, z3) + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', 0, z3) + s9 :|: s9 >= 0, s9 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 1 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', z'' - 1, z3) + s8 :|: s8 >= 0, s8 <= 1 + (z'' - 1), z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', z'' - 1, z3) + 1 :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + s14 :|: s14 >= 0, s14 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + s13 :|: s13 >= 0, s13 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) + 1 :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND1(2, 0, z'', 0) + s12 :|: s12 >= 0, s12 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, 0, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND1(2, z' - 1, z'', 0) + s11 :|: s11 >= 0, s11 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, z' - 1, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(1, 0, z'', z3) + s10 :|: s10 >= 0, s10 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(1, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, 0, z'', z3) + s15 :|: s15 >= 0, s15 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, 0, z'', z3) + s17 :|: s17 >= 0, s17 <= z', z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 1 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, z' - 1, z'', z3) + s16 :|: s16 >= 0, s16 <= 1 + (z' - 1), z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, z' - 1, z'', z3) + 1 :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s18 :|: s18 >= 0, s18 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', 0, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(gr(z'' - 1, z3 - 1), z', z'' - 1, 1 + (z3 - 1)) :|: z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), 0, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(gr(z' - 1, z3 - 1), z' - 1, z'', 1 + (z3 - 1)) :|: z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> 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: {p}, {COND2,COND1}, {cond2,cond1}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  gr: runtime: O(1) [0], size: O(1) [2]

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

(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'', z3) -{ 3 + z3 }-> 1 + COND2(s19, z', 1 + (z'' - 1), 1 + (z3 - 1)) + s'' :|: s19 >= 0, s19 <= 2, s'' >= 0, s'' <= 1 + (z'' - 1), z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', 1 + (z'' - 1), 0) + s' :|: s' >= 0, s' <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(1, z', 0, z3) + s :|: s >= 0, s <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', z'', z3) + s1 :|: s1 >= 0, s1 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(s20, z', z'' - 1, 1 + (z3 - 1)) + s5 :|: s20 >= 0, s20 <= 2, s5 >= 0, s5 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(s21, z', 0, 1 + (z3 - 1)) + s6 :|: s21 >= 0, s21 <= 2, s6 >= 0, s6 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(s30, z', z'' - 1, 1 + (z3 - 1)) + 1 :|: s30 >= 0, s30 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(s31, z', 0, 1 + (z3 - 1)) + 1 :|: s31 >= 0, s31 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', 0, 0) + s4 :|: s4 >= 0, s4 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', 0, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', z'' - 1, 0) + s3 :|: s3 >= 0, s3 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', z'' - 1, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(1, z', 0, z3) + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(1, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', 0, z3) + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', 0, z3) + s9 :|: s9 >= 0, s9 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 1 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', z'' - 1, z3) + s8 :|: s8 >= 0, s8 <= 1 + (z'' - 1), z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', z'' - 1, z3) + 1 :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(s22, z' - 1, z'', 1 + (z3 - 1)) + s13 :|: s22 >= 0, s22 <= 2, s13 >= 0, s13 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(s23, 0, z'', 1 + (z3 - 1)) + s14 :|: s23 >= 0, s23 <= 2, s14 >= 0, s14 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(s32, z' - 1, z'', 1 + (z3 - 1)) + 1 :|: s32 >= 0, s32 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(s33, 0, z'', 1 + (z3 - 1)) + 1 :|: s33 >= 0, s33 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND1(2, 0, z'', 0) + s12 :|: s12 >= 0, s12 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, 0, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND1(2, z' - 1, z'', 0) + s11 :|: s11 >= 0, s11 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, z' - 1, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(1, 0, z'', z3) + s10 :|: s10 >= 0, s10 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(1, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, 0, z'', z3) + s15 :|: s15 >= 0, s15 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, 0, z'', z3) + s17 :|: s17 >= 0, s17 <= z', z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 1 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, z' - 1, z'', z3) + s16 :|: s16 >= 0, s16 <= 1 + (z' - 1), z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, z' - 1, z'', z3) + 1 :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s18 :|: s18 >= 0, s18 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(s24, z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: s24 >= 0, s24 <= 2, z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(s25, z', z'' - 1, 1 + (z3 - 1)) :|: s25 >= 0, s25 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(s26, z', 0, 1 + (z3 - 1)) :|: s26 >= 0, s26 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(s27, z' - 1, z'', 1 + (z3 - 1)) :|: s27 >= 0, s27 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(s28, 0, z'', 1 + (z3 - 1)) :|: s28 >= 0, s28 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> s29 :|: s29 >= 0, s29 <= 2, 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}, {COND2,COND1}, {cond2,cond1}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  gr: runtime: O(1) [0], size: O(1) [2]

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

(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'', z3) -{ 3 + z3 }-> 1 + COND2(s19, z', 1 + (z'' - 1), 1 + (z3 - 1)) + s'' :|: s19 >= 0, s19 <= 2, s'' >= 0, s'' <= 1 + (z'' - 1), z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', 1 + (z'' - 1), 0) + s' :|: s' >= 0, s' <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(1, z', 0, z3) + s :|: s >= 0, s <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', z'', z3) + s1 :|: s1 >= 0, s1 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(s20, z', z'' - 1, 1 + (z3 - 1)) + s5 :|: s20 >= 0, s20 <= 2, s5 >= 0, s5 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(s21, z', 0, 1 + (z3 - 1)) + s6 :|: s21 >= 0, s21 <= 2, s6 >= 0, s6 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(s30, z', z'' - 1, 1 + (z3 - 1)) + 1 :|: s30 >= 0, s30 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(s31, z', 0, 1 + (z3 - 1)) + 1 :|: s31 >= 0, s31 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', 0, 0) + s4 :|: s4 >= 0, s4 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', 0, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', z'' - 1, 0) + s3 :|: s3 >= 0, s3 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', z'' - 1, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(1, z', 0, z3) + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(1, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', 0, z3) + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', 0, z3) + s9 :|: s9 >= 0, s9 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 1 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', z'' - 1, z3) + s8 :|: s8 >= 0, s8 <= 1 + (z'' - 1), z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', z'' - 1, z3) + 1 :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(s22, z' - 1, z'', 1 + (z3 - 1)) + s13 :|: s22 >= 0, s22 <= 2, s13 >= 0, s13 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(s23, 0, z'', 1 + (z3 - 1)) + s14 :|: s23 >= 0, s23 <= 2, s14 >= 0, s14 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(s32, z' - 1, z'', 1 + (z3 - 1)) + 1 :|: s32 >= 0, s32 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(s33, 0, z'', 1 + (z3 - 1)) + 1 :|: s33 >= 0, s33 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND1(2, 0, z'', 0) + s12 :|: s12 >= 0, s12 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, 0, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND1(2, z' - 1, z'', 0) + s11 :|: s11 >= 0, s11 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, z' - 1, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(1, 0, z'', z3) + s10 :|: s10 >= 0, s10 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(1, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, 0, z'', z3) + s15 :|: s15 >= 0, s15 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, 0, z'', z3) + s17 :|: s17 >= 0, s17 <= z', z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 1 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, z' - 1, z'', z3) + s16 :|: s16 >= 0, s16 <= 1 + (z' - 1), z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, z' - 1, z'', z3) + 1 :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s18 :|: s18 >= 0, s18 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(s24, z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: s24 >= 0, s24 <= 2, z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(s25, z', z'' - 1, 1 + (z3 - 1)) :|: s25 >= 0, s25 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(s26, z', 0, 1 + (z3 - 1)) :|: s26 >= 0, s26 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(s27, z' - 1, z'', 1 + (z3 - 1)) :|: s27 >= 0, s27 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(s28, 0, z'', 1 + (z3 - 1)) :|: s28 >= 0, s28 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> s29 :|: s29 >= 0, s29 <= 2, 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}, {COND2,COND1}, {cond2,cond1}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  gr: runtime: O(1) [0], size: O(1) [2]
  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'', z3) -{ 3 + z3 }-> 1 + COND2(s19, z', 1 + (z'' - 1), 1 + (z3 - 1)) + s'' :|: s19 >= 0, s19 <= 2, s'' >= 0, s'' <= 1 + (z'' - 1), z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', 1 + (z'' - 1), 0) + s' :|: s' >= 0, s' <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(1, z', 0, z3) + s :|: s >= 0, s <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', z'', z3) + s1 :|: s1 >= 0, s1 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(s20, z', z'' - 1, 1 + (z3 - 1)) + s5 :|: s20 >= 0, s20 <= 2, s5 >= 0, s5 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(s21, z', 0, 1 + (z3 - 1)) + s6 :|: s21 >= 0, s21 <= 2, s6 >= 0, s6 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(s30, z', z'' - 1, 1 + (z3 - 1)) + 1 :|: s30 >= 0, s30 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(s31, z', 0, 1 + (z3 - 1)) + 1 :|: s31 >= 0, s31 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', 0, 0) + s4 :|: s4 >= 0, s4 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', 0, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', z'' - 1, 0) + s3 :|: s3 >= 0, s3 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', z'' - 1, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(1, z', 0, z3) + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(1, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', 0, z3) + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', 0, z3) + s9 :|: s9 >= 0, s9 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 1 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', z'' - 1, z3) + s8 :|: s8 >= 0, s8 <= 1 + (z'' - 1), z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', z'' - 1, z3) + 1 :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(s22, z' - 1, z'', 1 + (z3 - 1)) + s13 :|: s22 >= 0, s22 <= 2, s13 >= 0, s13 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(s23, 0, z'', 1 + (z3 - 1)) + s14 :|: s23 >= 0, s23 <= 2, s14 >= 0, s14 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(s32, z' - 1, z'', 1 + (z3 - 1)) + 1 :|: s32 >= 0, s32 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(s33, 0, z'', 1 + (z3 - 1)) + 1 :|: s33 >= 0, s33 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND1(2, 0, z'', 0) + s12 :|: s12 >= 0, s12 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, 0, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND1(2, z' - 1, z'', 0) + s11 :|: s11 >= 0, s11 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, z' - 1, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(1, 0, z'', z3) + s10 :|: s10 >= 0, s10 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(1, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, 0, z'', z3) + s15 :|: s15 >= 0, s15 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, 0, z'', z3) + s17 :|: s17 >= 0, s17 <= z', z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 1 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, z' - 1, z'', z3) + s16 :|: s16 >= 0, s16 <= 1 + (z' - 1), z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, z' - 1, z'', z3) + 1 :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s18 :|: s18 >= 0, s18 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(s24, z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: s24 >= 0, s24 <= 2, z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(s25, z', z'' - 1, 1 + (z3 - 1)) :|: s25 >= 0, s25 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(s26, z', 0, 1 + (z3 - 1)) :|: s26 >= 0, s26 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(s27, z' - 1, z'', 1 + (z3 - 1)) :|: s27 >= 0, s27 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(s28, 0, z'', 1 + (z3 - 1)) :|: s28 >= 0, s28 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> s29 :|: s29 >= 0, s29 <= 2, 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}, {cond2,cond1}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  gr: runtime: O(1) [0], size: O(1) [2]
  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'', z3) -{ 3 + z3 }-> 1 + COND2(s19, z', 1 + (z'' - 1), 1 + (z3 - 1)) + s'' :|: s19 >= 0, s19 <= 2, s'' >= 0, s'' <= 1 + (z'' - 1), z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', 1 + (z'' - 1), 0) + s' :|: s' >= 0, s' <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(1, z', 0, z3) + s :|: s >= 0, s <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', z'', z3) + s1 :|: s1 >= 0, s1 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(s20, z', z'' - 1, 1 + (z3 - 1)) + s5 :|: s20 >= 0, s20 <= 2, s5 >= 0, s5 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(s21, z', 0, 1 + (z3 - 1)) + s6 :|: s21 >= 0, s21 <= 2, s6 >= 0, s6 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(s30, z', z'' - 1, 1 + (z3 - 1)) + 1 :|: s30 >= 0, s30 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(s31, z', 0, 1 + (z3 - 1)) + 1 :|: s31 >= 0, s31 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', 0, 0) + s4 :|: s4 >= 0, s4 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', 0, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', z'' - 1, 0) + s3 :|: s3 >= 0, s3 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', z'' - 1, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(1, z', 0, z3) + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(1, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', 0, z3) + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', 0, z3) + s9 :|: s9 >= 0, s9 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 1 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', z'' - 1, z3) + s8 :|: s8 >= 0, s8 <= 1 + (z'' - 1), z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', z'' - 1, z3) + 1 :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(s22, z' - 1, z'', 1 + (z3 - 1)) + s13 :|: s22 >= 0, s22 <= 2, s13 >= 0, s13 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(s23, 0, z'', 1 + (z3 - 1)) + s14 :|: s23 >= 0, s23 <= 2, s14 >= 0, s14 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(s32, z' - 1, z'', 1 + (z3 - 1)) + 1 :|: s32 >= 0, s32 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(s33, 0, z'', 1 + (z3 - 1)) + 1 :|: s33 >= 0, s33 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND1(2, 0, z'', 0) + s12 :|: s12 >= 0, s12 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, 0, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND1(2, z' - 1, z'', 0) + s11 :|: s11 >= 0, s11 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, z' - 1, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(1, 0, z'', z3) + s10 :|: s10 >= 0, s10 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(1, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, 0, z'', z3) + s15 :|: s15 >= 0, s15 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, 0, z'', z3) + s17 :|: s17 >= 0, s17 <= z', z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 1 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, z' - 1, z'', z3) + s16 :|: s16 >= 0, s16 <= 1 + (z' - 1), z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, z' - 1, z'', z3) + 1 :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s18 :|: s18 >= 0, s18 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(s24, z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: s24 >= 0, s24 <= 2, z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(s25, z', z'' - 1, 1 + (z3 - 1)) :|: s25 >= 0, s25 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(s26, z', 0, 1 + (z3 - 1)) :|: s26 >= 0, s26 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(s27, z' - 1, z'', 1 + (z3 - 1)) :|: s27 >= 0, s27 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(s28, 0, z'', 1 + (z3 - 1)) :|: s28 >= 0, s28 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> s29 :|: s29 >= 0, s29 <= 2, 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}, {cond2,cond1}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  gr: runtime: O(1) [0], size: O(1) [2]
  p: runtime: O(1) [0], size: O(n^1) [z]

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

(45) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT 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(n^1) with polynomial bound: 1 + z''

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

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

   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(s19, z', 1 + (z'' - 1), 1 + (z3 - 1)) + s'' :|: s19 >= 0, s19 <= 2, s'' >= 0, s'' <= 1 + (z'' - 1), z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', 1 + (z'' - 1), 0) + s' :|: s' >= 0, s' <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(1, z', 0, z3) + s :|: s >= 0, s <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', z'', z3) + s1 :|: s1 >= 0, s1 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(s20, z', z'' - 1, 1 + (z3 - 1)) + s5 :|: s20 >= 0, s20 <= 2, s5 >= 0, s5 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(s21, z', 0, 1 + (z3 - 1)) + s6 :|: s21 >= 0, s21 <= 2, s6 >= 0, s6 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(s30, z', z'' - 1, 1 + (z3 - 1)) + 1 :|: s30 >= 0, s30 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(s31, z', 0, 1 + (z3 - 1)) + 1 :|: s31 >= 0, s31 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', 0, 0) + s4 :|: s4 >= 0, s4 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', 0, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', z'' - 1, 0) + s3 :|: s3 >= 0, s3 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', z'' - 1, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(1, z', 0, z3) + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(1, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', 0, z3) + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', 0, z3) + s9 :|: s9 >= 0, s9 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 1 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', z'' - 1, z3) + s8 :|: s8 >= 0, s8 <= 1 + (z'' - 1), z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', z'' - 1, z3) + 1 :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(s22, z' - 1, z'', 1 + (z3 - 1)) + s13 :|: s22 >= 0, s22 <= 2, s13 >= 0, s13 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(s23, 0, z'', 1 + (z3 - 1)) + s14 :|: s23 >= 0, s23 <= 2, s14 >= 0, s14 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(s32, z' - 1, z'', 1 + (z3 - 1)) + 1 :|: s32 >= 0, s32 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(s33, 0, z'', 1 + (z3 - 1)) + 1 :|: s33 >= 0, s33 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND1(2, 0, z'', 0) + s12 :|: s12 >= 0, s12 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, 0, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND1(2, z' - 1, z'', 0) + s11 :|: s11 >= 0, s11 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, z' - 1, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(1, 0, z'', z3) + s10 :|: s10 >= 0, s10 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(1, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, 0, z'', z3) + s15 :|: s15 >= 0, s15 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, 0, z'', z3) + s17 :|: s17 >= 0, s17 <= z', z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 1 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, z' - 1, z'', z3) + s16 :|: s16 >= 0, s16 <= 1 + (z' - 1), z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, z' - 1, z'', z3) + 1 :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s18 :|: s18 >= 0, s18 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(s24, z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: s24 >= 0, s24 <= 2, z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(s25, z', z'' - 1, 1 + (z3 - 1)) :|: s25 >= 0, s25 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(s26, z', 0, 1 + (z3 - 1)) :|: s26 >= 0, s26 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(s27, z' - 1, z'', 1 + (z3 - 1)) :|: s27 >= 0, s27 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(s28, 0, z'', 1 + (z3 - 1)) :|: s28 >= 0, s28 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> s29 :|: s29 >= 0, s29 <= 2, 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}, {cond2,cond1}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  gr: runtime: O(1) [0], size: O(1) [2]
  p: runtime: O(1) [0], size: O(n^1) [z]
  COND2: runtime: ?, size: O(1) [0]
  COND1: runtime: ?, size: O(n^1) [1 + z'']

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

(47) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: COND2
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 96*z + 15*z*z3 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3

Computed RUNTIME bound using KoAT for: COND1
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 492 + 1152*z' + 135*z'*z3 + 288*z'' + 30*z''*z3 + 48*z3

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

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

   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(s19, z', 1 + (z'' - 1), 1 + (z3 - 1)) + s'' :|: s19 >= 0, s19 <= 2, s'' >= 0, s'' <= 1 + (z'' - 1), z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', 1 + (z'' - 1), 0) + s' :|: s' >= 0, s' <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(1, z', 0, z3) + s :|: s >= 0, s <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', z'', z3) + s1 :|: s1 >= 0, s1 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(s20, z', z'' - 1, 1 + (z3 - 1)) + s5 :|: s20 >= 0, s20 <= 2, s5 >= 0, s5 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(s21, z', 0, 1 + (z3 - 1)) + s6 :|: s21 >= 0, s21 <= 2, s6 >= 0, s6 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(s30, z', z'' - 1, 1 + (z3 - 1)) + 1 :|: s30 >= 0, s30 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(s31, z', 0, 1 + (z3 - 1)) + 1 :|: s31 >= 0, s31 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', 0, 0) + s4 :|: s4 >= 0, s4 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', 0, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND2(2, z', z'' - 1, 0) + s3 :|: s3 >= 0, s3 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(2, z', z'' - 1, 0) + 1 :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(1, z', 0, z3) + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(1, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', 0, z3) + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', 0, z3) + s9 :|: s9 >= 0, s9 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 1 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', 0, z3) + 0 :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND2(0, z', z'' - 1, z3) + s8 :|: s8 >= 0, s8 <= 1 + (z'' - 1), z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND2(0, z', z'' - 1, z3) + 1 :|: z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(s22, z' - 1, z'', 1 + (z3 - 1)) + s13 :|: s22 >= 0, s22 <= 2, s13 >= 0, s13 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(s23, 0, z'', 1 + (z3 - 1)) + s14 :|: s23 >= 0, s23 <= 2, s14 >= 0, s14 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(s32, z' - 1, z'', 1 + (z3 - 1)) + 1 :|: s32 >= 0, s32 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(s33, 0, z'', 1 + (z3 - 1)) + 1 :|: s33 >= 0, s33 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND1(2, 0, z'', 0) + s12 :|: s12 >= 0, s12 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, 0, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 }-> 1 + COND1(2, z' - 1, z'', 0) + s11 :|: s11 >= 0, s11 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(2, z' - 1, z'', 0) + 1 :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(1, 0, z'', z3) + s10 :|: s10 >= 0, s10 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(1, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, 0, z'', z3) + s15 :|: s15 >= 0, s15 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, 0, z'', z3) + s17 :|: s17 >= 0, s17 <= z', z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 1 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, 0, z'', z3) + 0 :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ 3 + z3 }-> 1 + COND1(0, z' - 1, z'', z3) + s16 :|: s16 >= 0, s16 <= 1 + (z' - 1), z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 2 }-> 1 + COND1(0, z' - 1, z'', z3) + 1 :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s18 :|: s18 >= 0, s18 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(s24, z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: s24 >= 0, s24 <= 2, z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(s25, z', z'' - 1, 1 + (z3 - 1)) :|: s25 >= 0, s25 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(s26, z', 0, 1 + (z3 - 1)) :|: s26 >= 0, s26 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(s27, z' - 1, z'', 1 + (z3 - 1)) :|: s27 >= 0, s27 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(s28, 0, z'', 1 + (z3 - 1)) :|: s28 >= 0, s28 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> s29 :|: s29 >= 0, s29 <= 2, 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}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  gr: runtime: O(1) [0], size: O(1) [2]
  p: runtime: O(1) [0], size: O(n^1) [z]
  COND2: runtime: O(n^2) [96*z + 15*z*z3 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3], size: O(1) [0]
  COND1: runtime: O(n^2) [492 + 1152*z' + 135*z'*z3 + 288*z'' + 30*z''*z3 + 48*z3], size: O(n^1) [1 + z'']

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

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

(50)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'', z3) -{ 99 + 288*z' + 45*z'*z3 + 16*z3 }-> 1 + s34 + s :|: s34 >= 0, s34 <= 0, s >= 0, s <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 195 + 288*z' + 96*z'' }-> 1 + s35 + s' :|: s35 >= 0, s35 <= 0, s' >= 0, s' <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 3 + 96*s19 + 15*s19*z3 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3 + z3 }-> 1 + s36 + s'' :|: s36 >= 0, s36 <= 0, s19 >= 0, s19 <= 2, s'' >= 0, s'' <= 1 + (z'' - 1), z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 3 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3 + z3 }-> 1 + s37 + s1 :|: s37 >= 0, s37 <= 0, s1 >= 0, s1 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 99 + 288*z' + 45*z'*z3 + 16*z3 }-> 1 + s38 + s2 :|: s38 >= 0, s38 <= 0, s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 99 + 288*z' + 96*z'' }-> 1 + s39 + s3 :|: s39 >= 0, s39 <= 0, s3 >= 0, s3 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 195 + 288*z' }-> 1 + s40 + s4 :|: s40 >= 0, s40 <= 0, s4 >= 0, s4 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ -93 + 96*s20 + 15*s20*z3 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3 + -14*z3 }-> 1 + s41 + s5 :|: s41 >= 0, s41 <= 0, s20 >= 0, s20 <= 2, s5 >= 0, s5 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 3 + 96*s21 + 15*s21*z3 + 288*z' + 45*z'*z3 + z3 }-> 1 + s42 + s6 :|: s42 >= 0, s42 <= 0, s21 >= 0, s21 <= 2, s6 >= 0, s6 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 3 + 288*z' + 45*z'*z3 + z3 }-> 1 + s43 + s7 :|: s43 >= 0, s43 <= 0, s7 >= 0, s7 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ -93 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3 + -14*z3 }-> 1 + s44 + s8 :|: s44 >= 0, s44 <= 0, s8 >= 0, s8 <= 1 + (z'' - 1), z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + 288*z' + 45*z'*z3 + z3 }-> 1 + s45 + s9 :|: s45 >= 0, s45 <= 0, s9 >= 0, s9 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 495 + 288*z'' + 30*z''*z3 + 49*z3 }-> 1 + s46 + s10 :|: s46 >= 0, s46 <= z'' + 1, s10 >= 0, s10 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ -657 + 1152*z' + 288*z'' }-> 1 + s47 + s11 :|: s47 >= 0, s47 <= z'' + 1, s11 >= 0, s11 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 495 + 288*z'' }-> 1 + s48 + s12 :|: s48 >= 0, s48 <= z'' + 1, s12 >= 0, s12 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ -657 + 1152*z' + 135*z'*z3 + 288*z'' + 30*z''*z3 + -86*z3 }-> 1 + s49 + s13 :|: s49 >= 0, s49 <= z'' + 1, s22 >= 0, s22 <= 2, s13 >= 0, s13 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 495 + 288*z'' + 30*z''*z3 + 49*z3 }-> 1 + s50 + s14 :|: s50 >= 0, s50 <= z'' + 1, s23 >= 0, s23 <= 2, s14 >= 0, s14 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 495 + 288*z'' + 30*z''*z3 + 49*z3 }-> 1 + s51 + s15 :|: s51 >= 0, s51 <= z'' + 1, s15 >= 0, s15 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ -657 + 1152*z' + 135*z'*z3 + 288*z'' + 30*z''*z3 + -86*z3 }-> 1 + s52 + s16 :|: s52 >= 0, s52 <= z'' + 1, s16 >= 0, s16 <= 1 + (z' - 1), z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 495 + 288*z'' + 30*z''*z3 + 49*z3 }-> 1 + s53 + s17 :|: s53 >= 0, s53 <= z'' + 1, s17 >= 0, s17 <= z', z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 98 + 288*z' + 45*z'*z3 + 15*z3 }-> 1 + s54 + 0 :|: s54 >= 0, s54 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 98 + 288*z' + 96*z'' }-> 1 + s55 + 1 :|: s55 >= 0, s55 <= 0, z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 194 + 288*z' }-> 1 + s56 + 1 :|: s56 >= 0, s56 <= 0, z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ -94 + 96*s30 + 15*s30*z3 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3 + -15*z3 }-> 1 + s57 + 1 :|: s57 >= 0, s57 <= 0, s30 >= 0, s30 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 2 + 96*s31 + 15*s31*z3 + 288*z' + 45*z'*z3 }-> 1 + s58 + 1 :|: s58 >= 0, s58 <= 0, s31 >= 0, s31 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 2 + 288*z' + 45*z'*z3 }-> 1 + s59 + 0 :|: s59 >= 0, s59 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ -94 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3 + -15*z3 }-> 1 + s60 + 1 :|: s60 >= 0, s60 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 2 + 288*z' + 45*z'*z3 }-> 1 + s61 + 1 :|: s61 >= 0, s61 <= 0, z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 + 288*z' + 45*z'*z3 }-> 1 + s62 + 0 :|: s62 >= 0, s62 <= 0, z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 494 + 288*z'' + 30*z''*z3 + 48*z3 }-> 1 + s63 + 0 :|: s63 >= 0, s63 <= z'' + 1, z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ -658 + 1152*z' + 288*z'' }-> 1 + s64 + 1 :|: s64 >= 0, s64 <= z'' + 1, z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 494 + 288*z'' }-> 1 + s65 + 1 :|: s65 >= 0, s65 <= z'' + 1, z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ -658 + 1152*z' + 135*z'*z3 + 288*z'' + 30*z''*z3 + -87*z3 }-> 1 + s66 + 1 :|: s66 >= 0, s66 <= z'' + 1, s32 >= 0, s32 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 494 + 288*z'' + 30*z''*z3 + 48*z3 }-> 1 + s67 + 1 :|: s67 >= 0, s67 <= z'' + 1, s33 >= 0, s33 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 494 + 288*z'' + 30*z''*z3 + 48*z3 }-> 1 + s68 + 0 :|: s68 >= 0, s68 <= z'' + 1, z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ -658 + 1152*z' + 135*z'*z3 + 288*z'' + 30*z''*z3 + -87*z3 }-> 1 + s69 + 1 :|: s69 >= 0, s69 <= z'' + 1, z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 494 + 288*z'' + 30*z''*z3 + 48*z3 }-> 1 + s70 + 1 :|: s70 >= 0, s70 <= z'' + 1, z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 494 + 288*z'' + 30*z''*z3 + 48*z3 }-> 1 + s71 + 0 :|: s71 >= 0, s71 <= z'' + 1, z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s18 :|: s18 >= 0, s18 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(s24, z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: s24 >= 0, s24 <= 2, z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(s25, z', z'' - 1, 1 + (z3 - 1)) :|: s25 >= 0, s25 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(s26, z', 0, 1 + (z3 - 1)) :|: s26 >= 0, s26 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(s27, z' - 1, z'', 1 + (z3 - 1)) :|: s27 >= 0, s27 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(s28, 0, z'', 1 + (z3 - 1)) :|: s28 >= 0, s28 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> s29 :|: s29 >= 0, s29 <= 2, 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}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  gr: runtime: O(1) [0], size: O(1) [2]
  p: runtime: O(1) [0], size: O(n^1) [z]
  COND2: runtime: O(n^2) [96*z + 15*z*z3 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3], size: O(1) [0]
  COND1: runtime: O(n^2) [492 + 1152*z' + 135*z'*z3 + 288*z'' + 30*z''*z3 + 48*z3], size: O(n^1) [1 + z'']

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

(51) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT 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: 0

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

(52)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'', z3) -{ 99 + 288*z' + 45*z'*z3 + 16*z3 }-> 1 + s34 + s :|: s34 >= 0, s34 <= 0, s >= 0, s <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 195 + 288*z' + 96*z'' }-> 1 + s35 + s' :|: s35 >= 0, s35 <= 0, s' >= 0, s' <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 3 + 96*s19 + 15*s19*z3 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3 + z3 }-> 1 + s36 + s'' :|: s36 >= 0, s36 <= 0, s19 >= 0, s19 <= 2, s'' >= 0, s'' <= 1 + (z'' - 1), z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 3 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3 + z3 }-> 1 + s37 + s1 :|: s37 >= 0, s37 <= 0, s1 >= 0, s1 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 99 + 288*z' + 45*z'*z3 + 16*z3 }-> 1 + s38 + s2 :|: s38 >= 0, s38 <= 0, s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 99 + 288*z' + 96*z'' }-> 1 + s39 + s3 :|: s39 >= 0, s39 <= 0, s3 >= 0, s3 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 195 + 288*z' }-> 1 + s40 + s4 :|: s40 >= 0, s40 <= 0, s4 >= 0, s4 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ -93 + 96*s20 + 15*s20*z3 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3 + -14*z3 }-> 1 + s41 + s5 :|: s41 >= 0, s41 <= 0, s20 >= 0, s20 <= 2, s5 >= 0, s5 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 3 + 96*s21 + 15*s21*z3 + 288*z' + 45*z'*z3 + z3 }-> 1 + s42 + s6 :|: s42 >= 0, s42 <= 0, s21 >= 0, s21 <= 2, s6 >= 0, s6 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 3 + 288*z' + 45*z'*z3 + z3 }-> 1 + s43 + s7 :|: s43 >= 0, s43 <= 0, s7 >= 0, s7 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ -93 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3 + -14*z3 }-> 1 + s44 + s8 :|: s44 >= 0, s44 <= 0, s8 >= 0, s8 <= 1 + (z'' - 1), z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + 288*z' + 45*z'*z3 + z3 }-> 1 + s45 + s9 :|: s45 >= 0, s45 <= 0, s9 >= 0, s9 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 495 + 288*z'' + 30*z''*z3 + 49*z3 }-> 1 + s46 + s10 :|: s46 >= 0, s46 <= z'' + 1, s10 >= 0, s10 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ -657 + 1152*z' + 288*z'' }-> 1 + s47 + s11 :|: s47 >= 0, s47 <= z'' + 1, s11 >= 0, s11 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 495 + 288*z'' }-> 1 + s48 + s12 :|: s48 >= 0, s48 <= z'' + 1, s12 >= 0, s12 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ -657 + 1152*z' + 135*z'*z3 + 288*z'' + 30*z''*z3 + -86*z3 }-> 1 + s49 + s13 :|: s49 >= 0, s49 <= z'' + 1, s22 >= 0, s22 <= 2, s13 >= 0, s13 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 495 + 288*z'' + 30*z''*z3 + 49*z3 }-> 1 + s50 + s14 :|: s50 >= 0, s50 <= z'' + 1, s23 >= 0, s23 <= 2, s14 >= 0, s14 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 495 + 288*z'' + 30*z''*z3 + 49*z3 }-> 1 + s51 + s15 :|: s51 >= 0, s51 <= z'' + 1, s15 >= 0, s15 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ -657 + 1152*z' + 135*z'*z3 + 288*z'' + 30*z''*z3 + -86*z3 }-> 1 + s52 + s16 :|: s52 >= 0, s52 <= z'' + 1, s16 >= 0, s16 <= 1 + (z' - 1), z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 495 + 288*z'' + 30*z''*z3 + 49*z3 }-> 1 + s53 + s17 :|: s53 >= 0, s53 <= z'' + 1, s17 >= 0, s17 <= z', z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 98 + 288*z' + 45*z'*z3 + 15*z3 }-> 1 + s54 + 0 :|: s54 >= 0, s54 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 98 + 288*z' + 96*z'' }-> 1 + s55 + 1 :|: s55 >= 0, s55 <= 0, z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 194 + 288*z' }-> 1 + s56 + 1 :|: s56 >= 0, s56 <= 0, z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ -94 + 96*s30 + 15*s30*z3 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3 + -15*z3 }-> 1 + s57 + 1 :|: s57 >= 0, s57 <= 0, s30 >= 0, s30 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 2 + 96*s31 + 15*s31*z3 + 288*z' + 45*z'*z3 }-> 1 + s58 + 1 :|: s58 >= 0, s58 <= 0, s31 >= 0, s31 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 2 + 288*z' + 45*z'*z3 }-> 1 + s59 + 0 :|: s59 >= 0, s59 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ -94 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3 + -15*z3 }-> 1 + s60 + 1 :|: s60 >= 0, s60 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 2 + 288*z' + 45*z'*z3 }-> 1 + s61 + 1 :|: s61 >= 0, s61 <= 0, z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 + 288*z' + 45*z'*z3 }-> 1 + s62 + 0 :|: s62 >= 0, s62 <= 0, z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 494 + 288*z'' + 30*z''*z3 + 48*z3 }-> 1 + s63 + 0 :|: s63 >= 0, s63 <= z'' + 1, z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ -658 + 1152*z' + 288*z'' }-> 1 + s64 + 1 :|: s64 >= 0, s64 <= z'' + 1, z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 494 + 288*z'' }-> 1 + s65 + 1 :|: s65 >= 0, s65 <= z'' + 1, z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ -658 + 1152*z' + 135*z'*z3 + 288*z'' + 30*z''*z3 + -87*z3 }-> 1 + s66 + 1 :|: s66 >= 0, s66 <= z'' + 1, s32 >= 0, s32 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 494 + 288*z'' + 30*z''*z3 + 48*z3 }-> 1 + s67 + 1 :|: s67 >= 0, s67 <= z'' + 1, s33 >= 0, s33 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 494 + 288*z'' + 30*z''*z3 + 48*z3 }-> 1 + s68 + 0 :|: s68 >= 0, s68 <= z'' + 1, z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ -658 + 1152*z' + 135*z'*z3 + 288*z'' + 30*z''*z3 + -87*z3 }-> 1 + s69 + 1 :|: s69 >= 0, s69 <= z'' + 1, z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 494 + 288*z'' + 30*z''*z3 + 48*z3 }-> 1 + s70 + 1 :|: s70 >= 0, s70 <= z'' + 1, z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 494 + 288*z'' + 30*z''*z3 + 48*z3 }-> 1 + s71 + 0 :|: s71 >= 0, s71 <= z'' + 1, z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s18 :|: s18 >= 0, s18 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(s24, z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: s24 >= 0, s24 <= 2, z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(s25, z', z'' - 1, 1 + (z3 - 1)) :|: s25 >= 0, s25 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(s26, z', 0, 1 + (z3 - 1)) :|: s26 >= 0, s26 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(s27, z' - 1, z'', 1 + (z3 - 1)) :|: s27 >= 0, s27 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(s28, 0, z'', 1 + (z3 - 1)) :|: s28 >= 0, s28 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> s29 :|: s29 >= 0, s29 <= 2, 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}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  gr: runtime: O(1) [0], size: O(1) [2]
  p: runtime: O(1) [0], size: O(n^1) [z]
  COND2: runtime: O(n^2) [96*z + 15*z*z3 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3], size: O(1) [0]
  COND1: runtime: O(n^2) [492 + 1152*z' + 135*z'*z3 + 288*z'' + 30*z''*z3 + 48*z3], size: O(n^1) [1 + z'']
  cond2: runtime: ?, size: O(1) [0]
  cond1: runtime: ?, size: O(1) [0]

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

(53) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: cond2
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

Computed RUNTIME bound using CoFloCo for: cond1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

(54)
Obligation:
Complexity RNTS consisting of the following rules:

   COND1(z, z', z'', z3) -{ 99 + 288*z' + 45*z'*z3 + 16*z3 }-> 1 + s34 + s :|: s34 >= 0, s34 <= 0, s >= 0, s <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND1(z, z', z'', z3) -{ 195 + 288*z' + 96*z'' }-> 1 + s35 + s' :|: s35 >= 0, s35 <= 0, s' >= 0, s' <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND1(z, z', z'', z3) -{ 3 + 96*s19 + 15*s19*z3 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3 + z3 }-> 1 + s36 + s'' :|: s36 >= 0, s36 <= 0, s19 >= 0, s19 <= 2, s'' >= 0, s'' <= 1 + (z'' - 1), z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   COND1(z, z', z'', z3) -{ 3 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3 + z3 }-> 1 + s37 + s1 :|: s37 >= 0, s37 <= 0, s1 >= 0, s1 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 99 + 288*z' + 45*z'*z3 + 16*z3 }-> 1 + s38 + s2 :|: s38 >= 0, s38 <= 0, s2 >= 0, s2 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 99 + 288*z' + 96*z'' }-> 1 + s39 + s3 :|: s39 >= 0, s39 <= 0, s3 >= 0, s3 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ 195 + 288*z' }-> 1 + s40 + s4 :|: s40 >= 0, s40 <= 0, s4 >= 0, s4 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   COND2(z, z', z'', z3) -{ -93 + 96*s20 + 15*s20*z3 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3 + -14*z3 }-> 1 + s41 + s5 :|: s41 >= 0, s41 <= 0, s20 >= 0, s20 <= 2, s5 >= 0, s5 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 3 + 96*s21 + 15*s21*z3 + 288*z' + 45*z'*z3 + z3 }-> 1 + s42 + s6 :|: s42 >= 0, s42 <= 0, s21 >= 0, s21 <= 2, s6 >= 0, s6 <= 1 + (z'' - 1), z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 3 + 288*z' + 45*z'*z3 + z3 }-> 1 + s43 + s7 :|: s43 >= 0, s43 <= 0, s7 >= 0, s7 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ -93 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3 + -14*z3 }-> 1 + s44 + s8 :|: s44 >= 0, s44 <= 0, s8 >= 0, s8 <= 1 + (z'' - 1), z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 3 + 288*z' + 45*z'*z3 + z3 }-> 1 + s45 + s9 :|: s45 >= 0, s45 <= 0, s9 >= 0, s9 <= z'', z = 2, z'' >= 0, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 495 + 288*z'' + 30*z''*z3 + 49*z3 }-> 1 + s46 + s10 :|: s46 >= 0, s46 <= z'' + 1, s10 >= 0, s10 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ -657 + 1152*z' + 288*z'' }-> 1 + s47 + s11 :|: s47 >= 0, s47 <= z'' + 1, s11 >= 0, s11 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ 495 + 288*z'' }-> 1 + s48 + s12 :|: s48 >= 0, s48 <= z'' + 1, s12 >= 0, s12 <= 1 + (z' - 1), z'' >= 0, z' - 1 >= 0, z = 1, z3 = 0
   COND2(z, z', z'', z3) -{ -657 + 1152*z' + 135*z'*z3 + 288*z'' + 30*z''*z3 + -86*z3 }-> 1 + s49 + s13 :|: s49 >= 0, s49 <= z'' + 1, s22 >= 0, s22 <= 2, s13 >= 0, s13 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 495 + 288*z'' + 30*z''*z3 + 49*z3 }-> 1 + s50 + s14 :|: s50 >= 0, s50 <= z'' + 1, s23 >= 0, s23 <= 2, s14 >= 0, s14 <= 1 + (z' - 1), z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   COND2(z, z', z'', z3) -{ 495 + 288*z'' + 30*z''*z3 + 49*z3 }-> 1 + s51 + s15 :|: s51 >= 0, s51 <= z'' + 1, s15 >= 0, s15 <= 0, z'' >= 0, z = 1, z3 >= 0, z' = 0
   COND2(z, z', z'', z3) -{ -657 + 1152*z' + 135*z'*z3 + 288*z'' + 30*z''*z3 + -86*z3 }-> 1 + s52 + s16 :|: s52 >= 0, s52 <= z'' + 1, s16 >= 0, s16 <= 1 + (z' - 1), z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 495 + 288*z'' + 30*z''*z3 + 49*z3 }-> 1 + s53 + s17 :|: s53 >= 0, s53 <= z'' + 1, s17 >= 0, s17 <= z', z'' >= 0, z = 1, z' >= 0, z3 >= 0
   COND2(z, z', z'', z3) -{ 98 + 288*z' + 45*z'*z3 + 15*z3 }-> 1 + s54 + 0 :|: s54 >= 0, s54 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ 98 + 288*z' + 96*z'' }-> 1 + s55 + 1 :|: s55 >= 0, s55 <= 0, z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 194 + 288*z' }-> 1 + s56 + 1 :|: s56 >= 0, s56 <= 0, z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ -94 + 96*s30 + 15*s30*z3 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3 + -15*z3 }-> 1 + s57 + 1 :|: s57 >= 0, s57 <= 0, s30 >= 0, s30 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 2 + 96*s31 + 15*s31*z3 + 288*z' + 45*z'*z3 }-> 1 + s58 + 1 :|: s58 >= 0, s58 <= 0, s31 >= 0, s31 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 2 + 288*z' + 45*z'*z3 }-> 1 + s59 + 0 :|: s59 >= 0, s59 <= 0, z = 2, z'' = 0, z' >= 0, z3 >= 0, 0 = 0
   COND2(z, z', z'', z3) -{ -94 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3 + -15*z3 }-> 1 + s60 + 1 :|: s60 >= 0, s60 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, z3 >= 0, 1 + (z'' - 1) = 1 + z0', z0' >= 0
   COND2(z, z', z'', z3) -{ 2 + 288*z' + 45*z'*z3 }-> 1 + s61 + 1 :|: s61 >= 0, s61 <= 0, z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' - 1 >= 0
   COND2(z, z', z'', z3) -{ 2 + 288*z' + 45*z'*z3 }-> 1 + s62 + 0 :|: s62 >= 0, s62 <= 0, z = 2, z'' >= 0, z' >= 0, z3 >= 0, z'' = 0
   COND2(z, z', z'', z3) -{ 494 + 288*z'' + 30*z''*z3 + 48*z3 }-> 1 + s63 + 0 :|: s63 >= 0, s63 <= z'' + 1, z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ -658 + 1152*z' + 288*z'' }-> 1 + s64 + 1 :|: s64 >= 0, s64 <= z'' + 1, z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 494 + 288*z'' }-> 1 + s65 + 1 :|: s65 >= 0, s65 <= z'' + 1, z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ -658 + 1152*z' + 135*z'*z3 + 288*z'' + 30*z''*z3 + -87*z3 }-> 1 + s66 + 1 :|: s66 >= 0, s66 <= z'' + 1, s32 >= 0, s32 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 494 + 288*z'' + 30*z''*z3 + 48*z3 }-> 1 + s67 + 1 :|: s67 >= 0, s67 <= z'' + 1, s33 >= 0, s33 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 494 + 288*z'' + 30*z''*z3 + 48*z3 }-> 1 + s68 + 0 :|: s68 >= 0, s68 <= z'' + 1, z'' >= 0, z = 1, z3 >= 0, z' = 0, 0 = 0
   COND2(z, z', z'', z3) -{ -658 + 1152*z' + 135*z'*z3 + 288*z'' + 30*z''*z3 + -87*z3 }-> 1 + s69 + 1 :|: s69 >= 0, s69 <= z'' + 1, z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND2(z, z', z'', z3) -{ 494 + 288*z'' + 30*z''*z3 + 48*z3 }-> 1 + s70 + 1 :|: s70 >= 0, s70 <= z'' + 1, z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' - 1 >= 0
   COND2(z, z', z'', z3) -{ 494 + 288*z'' + 30*z''*z3 + 48*z3 }-> 1 + s71 + 0 :|: s71 >= 0, s71 <= z'' + 1, z'' >= 0, z = 1, z' >= 0, z3 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s18 :|: s18 >= 0, s18 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(s24, z', 1 + (z'' - 1), 1 + (z3 - 1)) :|: s24 >= 0, s24 <= 2, z = 2, z'' - 1 >= 0, z' >= 0, z3 - 1 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(2, z', 1 + (z'' - 1), 0) :|: z = 2, z3 = 0, z'' - 1 >= 0, z' >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond1(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(s25, z', z'' - 1, 1 + (z3 - 1)) :|: s25 >= 0, s25 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(s26, z', 0, 1 + (z3 - 1)) :|: s26 >= 0, s26 <= 2, z = 2, z3 - 1 >= 0, z' >= 0, z'' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', 0, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(2, z', z'' - 1, 0) :|: z = 2, z'' - 1 >= 0, z3 = 0, z' >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(1, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' = 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', 0, z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond2(0, z', z'' - 1, z3) :|: z = 2, z' >= 0, z'' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(s27, z' - 1, z'', 1 + (z3 - 1)) :|: s27 >= 0, s27 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(s28, 0, z'', 1 + (z3 - 1)) :|: s28 >= 0, s28 <= 2, z' - 1 >= 0, z'' >= 0, z = 1, z3 - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, 0, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(2, z' - 1, z'', 0) :|: z'' >= 0, z = 1, z3 = 0, z' - 1 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(1, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z3 >= 0, z' = 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, 0, z'', z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> cond1(0, z' - 1, z'', z3) :|: z'' >= 0, z = 1, z' - 1 >= 0, z3 >= 0
   cond2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   gr(z, z') -{ 0 }-> s29 :|: s29 >= 0, s29 <= 2, 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:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  gr: runtime: O(1) [0], size: O(1) [2]
  p: runtime: O(1) [0], size: O(n^1) [z]
  COND2: runtime: O(n^2) [96*z + 15*z*z3 + 288*z' + 45*z'*z3 + 96*z'' + 15*z''*z3], size: O(1) [0]
  COND1: runtime: O(n^2) [492 + 1152*z' + 135*z'*z3 + 288*z'' + 30*z''*z3 + 48*z3], size: O(n^1) [1 + z'']
  cond2: runtime: O(1) [0], size: O(1) [0]
  cond1: runtime: O(1) [0], size: O(1) [0]

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(55) FinalProof (FINISHED)
Computed overall runtime complexity
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(56)
BOUNDS(1, n^2)

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(57) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
Transformed a relative TRS into a decreasing-loop problem.
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(58)
Obligation:
Analyzing the following TRS for decreasing loops:

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


The TRS R consists of the following rules:

   COND1(true, z0, z1, z2) -> c(COND2(gr(z1, z2), z0, z1, z2), GR(z1, z2))
   COND2(true, z0, z1, z2) -> c1(COND2(gr(z1, z2), z0, p(z1), z2), GR(z1, z2))
   COND2(true, z0, z1, z2) -> c2(COND2(gr(z1, z2), z0, p(z1), z2), P(z1))
   COND2(false, z0, z1, z2) -> c3(COND1(gr(z0, z2), p(z0), z1, z2), GR(z0, z2))
   COND2(false, z0, z1, z2) -> c4(COND1(gr(z0, z2), p(z0), z1, z2), 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

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

   cond1(true, z0, z1, z2) -> cond2(gr(z1, z2), z0, z1, z2)
   cond2(true, z0, z1, z2) -> cond2(gr(z1, z2), z0, p(z1), z2)
   cond2(false, z0, z1, z2) -> cond1(gr(z0, z2), p(z0), z1, z2)
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   p(0) -> 0
   p(s(z0)) -> z0

Rewrite Strategy: INNERMOST
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(59) DecreasingLoopProof (LOWER BOUND(ID))
The following loop(s) give(s) rise to the lower bound Omega(n^1):

The rewrite sequence

GR(s(z0), s(z1)) ->^+ c7(GR(z0, z1))

gives rise to a decreasing loop by considering the right hand sides subterm at position [0].

The pumping substitution is [z0 / s(z0), z1 / s(z1)].

The result substitution is [ ].




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(60)
Complex Obligation (BEST)

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(61)
Obligation:
Proved the lower bound n^1 for the following obligation:

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


The TRS R consists of the following rules:

   COND1(true, z0, z1, z2) -> c(COND2(gr(z1, z2), z0, z1, z2), GR(z1, z2))
   COND2(true, z0, z1, z2) -> c1(COND2(gr(z1, z2), z0, p(z1), z2), GR(z1, z2))
   COND2(true, z0, z1, z2) -> c2(COND2(gr(z1, z2), z0, p(z1), z2), P(z1))
   COND2(false, z0, z1, z2) -> c3(COND1(gr(z0, z2), p(z0), z1, z2), GR(z0, z2))
   COND2(false, z0, z1, z2) -> c4(COND1(gr(z0, z2), p(z0), z1, z2), 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

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

   cond1(true, z0, z1, z2) -> cond2(gr(z1, z2), z0, z1, z2)
   cond2(true, z0, z1, z2) -> cond2(gr(z1, z2), z0, p(z1), z2)
   cond2(false, z0, z1, z2) -> cond1(gr(z0, z2), p(z0), z1, z2)
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   p(0) -> 0
   p(s(z0)) -> z0

Rewrite Strategy: INNERMOST
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(62) LowerBoundPropagationProof (FINISHED)
Propagated lower bound.
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(63)
BOUNDS(n^1, INF)

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(64)
Obligation:
Analyzing the following TRS for decreasing loops:

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


The TRS R consists of the following rules:

   COND1(true, z0, z1, z2) -> c(COND2(gr(z1, z2), z0, z1, z2), GR(z1, z2))
   COND2(true, z0, z1, z2) -> c1(COND2(gr(z1, z2), z0, p(z1), z2), GR(z1, z2))
   COND2(true, z0, z1, z2) -> c2(COND2(gr(z1, z2), z0, p(z1), z2), P(z1))
   COND2(false, z0, z1, z2) -> c3(COND1(gr(z0, z2), p(z0), z1, z2), GR(z0, z2))
   COND2(false, z0, z1, z2) -> c4(COND1(gr(z0, z2), p(z0), z1, z2), 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

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

   cond1(true, z0, z1, z2) -> cond2(gr(z1, z2), z0, z1, z2)
   cond2(true, z0, z1, z2) -> cond2(gr(z1, z2), z0, p(z1), z2)
   cond2(false, z0, z1, z2) -> cond1(gr(z0, z2), p(z0), z1, z2)
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   p(0) -> 0
   p(s(z0)) -> z0

Rewrite Strategy: INNERMOST