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Complexity_ITS 2019-03-21 04.46 pair #429990332
details
property
value
status
complete
benchmark
ex27.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
13.7691 seconds
cpu usage
31.5201
user time
30.6891
system time
0.831025
max virtual memory
1.9351068E7
max residence set size
699276.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(1))
output
31.30/13.69 WORST_CASE(?, O(1)) 31.30/13.71 proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat 31.30/13.71 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 31.30/13.71 31.30/13.71 31.30/13.71 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). 31.30/13.71 31.30/13.71 (0) CpxIntTrs 31.30/13.71 (1) Koat Proof [FINISHED, 11.9 s] 31.30/13.71 (2) BOUNDS(1, 1) 31.30/13.71 31.30/13.71 31.30/13.71 ---------------------------------------- 31.30/13.71 31.30/13.71 (0) 31.30/13.71 Obligation: 31.30/13.71 Complexity Int TRS consisting of the following rules: 31.30/13.71 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f18(100, 0, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: TRUE 31.30/13.71 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f18(100, 10, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: TRUE 31.30/13.71 f18(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f21(A, B, B, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: 0 >= B + 1 31.30/13.71 f18(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f21(A, B, B, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: B >= 1 31.30/13.71 f18(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f46(A, 0, 0, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: B >= 0 && B <= 0 31.30/13.71 f21(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f27(A, B, C, 0, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: TRUE 31.30/13.71 f21(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f27(A, B, C, 10, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: TRUE 31.30/13.71 f27(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f46(A, B, C, 0, 0, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: D >= 0 && D <= 0 31.30/13.71 f27(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f30(A, B, C, D, D, 0, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: 0 >= D + 1 31.30/13.71 f27(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f30(A, B, C, D, D, 0, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: D >= 1 31.30/13.71 f46(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f58(A, B, C, D, E, F, 200, 0, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: TRUE 31.30/13.71 f46(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f58(A, B, C, D, E, F, 200, 10, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: TRUE 31.30/13.71 f58(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f61(A, B, C, D, E, F, G, H, H, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: 0 >= H + 1 31.30/13.71 f58(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f61(A, B, C, D, E, F, G, H, H, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: H >= 1 31.30/13.71 f58(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f86(A, B, C, D, E, F, G, 0, 0, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: H >= 0 && H <= 0 31.30/13.71 f61(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f67(A, B, C, D, E, F, G, H, I, 0, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: TRUE 31.30/13.71 f61(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f67(A, B, C, D, E, F, G, H, I, 10, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: TRUE 31.30/13.71 f67(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f86(A, B, C, D, E, F, G, H, I, 0, 0, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: J >= 0 && J <= 0 31.30/13.71 f67(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f70(A, B, C, D, E, F, G, H, I, J, J, 0, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: 0 >= J + 1 31.30/13.71 f67(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f70(A, B, C, D, E, F, G, H, I, J, J, 0, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: J >= 1 31.30/13.71 f86(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f98(A, B, C, D, E, F, G, H, I, J, K, L, 50, 0, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: TRUE 31.30/13.71 f86(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f98(A, B, C, D, E, F, G, H, I, J, K, L, 50, 10, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: TRUE 31.30/13.71 f98(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f101(A, B, C, D, E, F, G, H, I, J, K, L, M, N, N, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: 0 >= N + 1 31.30/13.71 f98(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f101(A, B, C, D, E, F, G, H, I, J, K, L, M, N, N, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: N >= 1 31.30/13.71 f98(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f126(A, B, C, D, E, F, G, H, I, J, K, L, M, 0, 0, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: N >= 0 && N <= 0 31.30/13.71 f101(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f107(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, 0, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: TRUE 31.30/13.71 f101(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f107(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, 10, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: TRUE 31.30/13.71 f107(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f126(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, 0, 0, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: P >= 0 && P <= 0 31.30/13.71 f107(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f110(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, P, 0, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: 0 >= P + 1 31.30/13.71 f107(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f110(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, P, 0, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: P >= 1 31.30/13.71 f126(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f138(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, 20, 0, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: TRUE 31.30/13.71 f126(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f138(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, 20, 10, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: TRUE 31.30/13.71 f138(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f141(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, T, V, W, X, Y, Z, A1, B1, C1, D1)) :|: 0 >= T + 1 31.30/13.71 f138(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f141(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, T, V, W, X, Y, Z, A1, B1, C1, D1)) :|: T >= 1 31.30/13.71 f138(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f166(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, 0, 0, V, W, X, Y, Z, A1, B1, C1, D1)) :|: T >= 0 && T <= 0 31.30/13.71 f141(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f147(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, 0, W, X, Y, Z, A1, B1, C1, D1)) :|: TRUE 31.30/13.71 f141(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f147(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, 10, W, X, Y, Z, A1, B1, C1, D1)) :|: TRUE 31.30/13.71 f147(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f166(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, 0, 0, X, Y, Z, A1, B1, C1, D1)) :|: V >= 0 && V <= 0 31.30/13.71 f147(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f150(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, V, 0, Y, Z, A1, B1, C1, D1)) :|: 0 >= V + 1 31.30/13.71 f147(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f150(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, V, 0, Y, Z, A1, B1, C1, D1)) :|: V >= 1 31.30/13.71 f166(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f178(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, 200, 0, A1, B1, C1, D1)) :|: TRUE 31.30/13.71 f166(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f178(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, 200, 10, A1, B1, C1, D1)) :|: TRUE 31.30/13.71 f178(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f181(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, Z, B1, C1, D1)) :|: 0 >= Z + 1 31.30/13.71 f178(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f181(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, Z, B1, C1, D1)) :|: Z >= 1 31.30/13.71 f181(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f187(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, 0, C1, D1)) :|: TRUE 31.30/13.71 f181(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f187(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, 10, C1, D1)) :|: TRUE 31.30/13.71 f187(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f190(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, B1, 0)) :|: 0 >= B1 + 1 31.30/13.71 f187(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f190(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, B1, 0)) :|: B1 >= 1 31.30/13.71 f178(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f207(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, 0, 0, B1, C1, D1)) :|: Z >= 0 && Z <= 0 31.30/13.71 f187(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f207(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, 0, 0, D1)) :|: B1 >= 0 && B1 <= 0 31.30/13.71 f190(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f190(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1 + 1)) :|: Y >= D1 + 1 31.30/13.71 f190(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f207(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: D1 >= Y 31.30/13.71 f150(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f150(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X + 1, Y, Z, A1, B1, C1, D1)) :|: S >= X + 1 31.30/13.71 f150(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f166(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: X >= S 31.30/13.71 f110(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f110(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R + 1, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: M >= R + 1 31.30/13.71 f110(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f126(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: R >= M 31.30/13.71 f70(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f70(A, B, C, D, E, F, G, H, I, J, K, L + 1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: G >= L + 1 31.30/13.71 f70(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f86(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: L >= G 31.30/13.71 f30(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f30(A, B, C, D, E, F + 1, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: A >= F + 1 31.30/13.71 f30(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1) -> Com_1(f46(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1)) :|: F >= A 31.30/13.71 31.30/13.71 The start-symbols are:[f0_30] 31.30/13.71 31.30/13.71 31.30/13.71 ---------------------------------------- 31.30/13.71 31.30/13.71 (1) Koat Proof (FINISHED) 31.30/13.71 YES(?, 50635) 31.30/13.71 31.30/13.71 31.30/13.71 31.30/13.71 Initial complexity problem: 31.30/13.71 31.30/13.71 1: T: 31.30/13.71 31.30/13.71 (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, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23, ar_24, ar_25, ar_26, ar_27, ar_28, ar_29) -> Com_1(f18(100, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23, ar_24, ar_25, ar_26, ar_27, ar_28, ar_29)) 31.30/13.71 31.30/13.71 (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, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23, ar_24, ar_25, ar_26, ar_27, ar_28, ar_29) -> Com_1(f18(100, 10, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23, ar_24, ar_25, ar_26, ar_27, ar_28, ar_29)) 31.30/13.71 31.30/13.71 (Comp: ?, Cost: 1) f18(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_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23, ar_24, ar_25, ar_26, ar_27, ar_28, ar_29) -> Com_1(f21(ar_0, ar_1, ar_1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23, ar_24, ar_25, ar_26, ar_27, ar_28, ar_29)) [ 0 >= ar_1 + 1 ] 31.30/13.71 31.30/13.71 (Comp: ?, Cost: 1) f18(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_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23, ar_24, ar_25, ar_26, ar_27, ar_28, ar_29) -> Com_1(f21(ar_0, ar_1, ar_1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23, ar_24, ar_25, ar_26, ar_27, ar_28, ar_29)) [ ar_1 >= 1 ] 31.30/13.71
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