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Compl Integ Trans Syste 26843 pair #381745452
details
property
value
status
complete
benchmark
graycode.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n098.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.00857305527 seconds
cpu usage
19.663951383
max memory
6.23456256E8
stage attributes
key
value
output-size
543102
starexec-result
WORST_CASE(?, O(1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 5362 ms] (2) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f62(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f63(A, B, C, D, E, F, G, H, I, J, K, L)) :|: 0 >= A + 1 f62(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f63(A, B, C, D, E, F, G, H, I, J, K, L)) :|: A >= 1 f0(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f13(1, 12, 1, 1, M, 0, G, H, I, J, K, L)) :|: TRUE f13(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f13(A, B, C, D, E, F + 1, G, H, I, J, K, L)) :|: B >= F + 1 f19(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f22(A, B, C, D, E, F, G, H, I, J, K, L)) :|: 0 >= C + 1 && B >= F + 1 f19(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f22(A, B, C, D, E, F, G, H, I, J, K, L)) :|: C >= 1 && B >= F + 1 f22(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f19(A, B, 1, D, E, F + 1, 1, H, I, J, K, L)) :|: M >= 0 && B >= N + 1 f22(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f19(A, B, 0, D, E, F + 1, 0, H, I, J, K, L)) :|: M >= 0 f22(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f19(A, B, 0, D, E, F + 1, 0, H, I, J, K, L)) :|: 0 >= M + 1 f19(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f19(A, B, 0, D, E, F + 1, 0, H, I, J, K, L)) :|: B >= F + 1 && C >= 0 && C <= 0 f32(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f35(A, B, C, D, E, F, G, F + 1, I, J, K, L)) :|: B >= 2 + F f35(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f38(A, B, C, D, E, F, G, H, I, J, K, L)) :|: 0 >= A + 1 && B >= H + 1 f35(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f38(A, B, C, D, E, F, G, H, I, J, K, L)) :|: A >= 1 && B >= H + 1 f38(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f35(1, B, C, D, E, F, G, H + 1, 1, J, K, L)) :|: M >= N + 1 f38(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f35(1, B, C, D, E, F, G, H + 1, 1, J, K, L)) :|: TRUE f38(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f35(0, B, C, D, E, F, G, H + 1, 0, J, K, L)) :|: TRUE f35(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f35(0, B, C, D, E, F, G, H + 1, 0, J, K, L)) :|: B >= H + 1 && A >= 0 && A <= 0 f48(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f52(A, B, C, D, E, F, G, H, I, M, K, L)) :|: 0 >= D + 1 && B >= 2 + F f48(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f52(A, B, C, D, E, F, G, H, I, M, K, L)) :|: D >= 1 && B >= 2 + F f52(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f48(A, B, C, 1, E, F + 1, G, H, I, J, 1, L)) :|: 0 >= J + 1 f52(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f48(A, B, C, 1, E, F + 1, G, H, I, J, 1, L)) :|: J >= 1 f52(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f48(A, B, C, 0, E, F + 1, G, H, I, 0, 0, L)) :|: J >= 0 && J <= 0 f52(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f48(A, B, C, 0, E, F + 1, G, H, I, J, 0, L)) :|: TRUE f48(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f48(A, B, C, 0, E, F + 1, G, H, I, M, 0, L)) :|: B >= 2 + F && D >= 0 && D <= 0 f63(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f71(A, B, C, D, E, F, G, H, I, J, K, 0)) :|: 0 >= D + 1 f63(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f71(A, B, C, D, E, F, G, H, I, J, K, 0)) :|: D >= 1 f63(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f71(A, B, C, 0, E, F, G, H, I, J, K, 1)) :|: D >= 0 && D <= 0 f62(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f71(0, B, C, D, E, F, G, H, I, J, K, 1)) :|: A >= 0 && A <= 0 f48(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f62(A, B, C, D, E, F, G, H, I, J, K, L)) :|: 0 >= C + 1 && F + 1 >= B f48(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f62(A, B, C, D, E, F, G, H, I, J, K, L)) :|: C >= 1 && F + 1 >= B f48(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f71(A, B, 0, D, E, F, G, H, I, J, K, 1)) :|: F + 1 >= B && C >= 0 && C <= 0 f35(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f32(A, B, C, D, E, F + 1, G, H, I, J, K, L)) :|: H >= B f32(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f48(A, B, C, D, E, 0, G, H, I, J, K, L)) :|: F + 1 >= B f19(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f32(A, B, C, D, E, 0, G, H, I, J, K, L)) :|: F >= B f13(A, B, C, D, E, F, G, H, I, J, K, L) -> Com_1(f19(A, B, C, D, E, 0, G, H, I, J, K, L)) :|: F >= B The start-symbols are:[f0_12] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 117828853) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_0 >= 1 ] (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(f13(1, 12, 1, 1, m, 0, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_1 >= ar_5 + 1 ] (Comp: ?, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_2 + 1 /\ ar_1 >= ar_5 + 1 ] (Comp: ?, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_2 >= 1 /\ ar_1 >= ar_5 + 1 ] (Comp: ?, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(f19(ar_0, ar_1, 1, ar_3, ar_4, ar_5 + 1, 1, ar_7, ar_8, ar_9, ar_10, ar_11)) [ m >= 0 /\ ar_1 >= n + 1 ] (Comp: ?, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(f19(ar_0, ar_1, 0, ar_3, ar_4, ar_5 + 1, 0, ar_7, ar_8, ar_9, ar_10, ar_11)) [ m >= 0 ] (Comp: ?, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(f19(ar_0, ar_1, 0, ar_3, ar_4, ar_5 + 1, 0, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= m + 1 ] (Comp: ?, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(f19(ar_0, ar_1, 0, ar_3, ar_4, ar_5 + 1, 0, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_1 >= ar_5 + 1 /\ ar_2 = 0 ] (Comp: ?, Cost: 1) f32(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_5 + 1, ar_8, ar_9, ar_10, ar_11)) [ ar_1 >= ar_5 + 2 ] (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(f38(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_0 + 1 /\ ar_1 >= ar_7 + 1 ] (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(f38(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_0 >= 1 /\ ar_1 >= ar_7 + 1 ] (Comp: ?, Cost: 1) f38(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(f35(1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, 1, ar_9, ar_10, ar_11)) [ m >= n + 1 ]
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