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Complexity_ITS 2019-03-21 04.46 pair #429991052
details
property
value
status
complete
benchmark
ex04.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n166.star.cs.uiowa.edu
space
ABC
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.02489 seconds
cpu usage
7.72506
user time
7.36545
system time
0.359613
max virtual memory
1.8617852E7
max residence set size
226148.0
stage attributes
key
value
starexec-result
MAYBE
output
7.64/3.98 MAYBE 7.66/3.99 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 7.66/3.99 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.66/3.99 7.66/3.99 7.66/3.99 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF). 7.66/3.99 7.66/3.99 (0) CpxIntTrs 7.66/3.99 (1) Loat Proof [FINISHED, 1728 ms] 7.66/3.99 (2) BOUNDS(1, INF) 7.66/3.99 7.66/3.99 7.66/3.99 ---------------------------------------- 7.66/3.99 7.66/3.99 (0) 7.66/3.99 Obligation: 7.66/3.99 Complexity Int TRS consisting of the following rules: 7.66/3.99 evalfstart(A, B, C, D) -> Com_1(evalfentryin(A, B, C, D)) :|: TRUE 7.66/3.99 evalfentryin(A, B, C, D) -> Com_1(evalfbb7in(0, B, C, D)) :|: TRUE 7.66/3.99 evalfbb7in(A, B, C, D) -> Com_1(evalfbb5in(A, B, 0, D)) :|: B * B * B >= 0 && 0 >= B * B * B && 0 >= 1 + A 7.66/3.99 evalfbb7in(A, B, C, D) -> Com_1(evalfbb5in(A, B, 0, D)) :|: B * B * B >= 1 && E >= 0 && B * B * B >= 2 * E && 1 + 2 * E >= B * B * B && E >= 1 + A 7.66/3.99 evalfbb7in(A, B, C, D) -> Com_1(evalfbb5in(A, B, 0, D)) :|: 0 >= B * B * B + 1 && 0 >= E && E >= 1 + A && 2 * E >= B * B * B && 1 + B * B * B >= 2 * E 7.66/3.99 evalfbb7in(A, B, C, D) -> Com_1(evalfreturnin(A, B, C, D)) :|: B * B * B >= 0 && 0 >= B * B * B && A >= 0 7.66/3.99 evalfbb7in(A, B, C, D) -> Com_1(evalfreturnin(A, B, C, D)) :|: B * B * B >= 1 && E >= 0 && B * B * B >= 2 * E && 1 + 2 * E >= B * B * B && A >= E 7.66/3.99 evalfbb7in(A, B, C, D) -> Com_1(evalfreturnin(A, B, C, D)) :|: 0 >= B * B * B + 1 && 0 >= E && A >= E && 2 * E >= B * B * B && 1 + B * B * B >= 2 * E 7.66/3.99 evalfbb5in(A, B, C, D) -> Com_1(evalfbb3in(A, B, C, 0)) :|: B >= 1 + C 7.66/3.99 evalfbb5in(A, B, C, D) -> Com_1(evalfbb6in(A, B, C, D)) :|: C >= B 7.66/3.99 evalfbb3in(A, B, C, D) -> Com_1(evalfbb2in(A, B, C, D)) :|: C >= 1 + D 7.66/3.99 evalfbb3in(A, B, C, D) -> Com_1(evalfbb4in(A, B, C, D)) :|: D >= C 7.66/3.99 evalfbb2in(A, B, C, D) -> Com_1(evalfbb3in(A, B, C, D + 1)) :|: TRUE 7.66/3.99 evalfbb4in(A, B, C, D) -> Com_1(evalfbb5in(A, B, C + 1, D)) :|: TRUE 7.66/3.99 evalfbb6in(A, B, C, D) -> Com_1(evalfbb7in(A + 1, B, C, D)) :|: TRUE 7.66/3.99 evalfreturnin(A, B, C, D) -> Com_1(evalfstop(A, B, C, D)) :|: TRUE 7.66/3.99 7.66/3.99 The start-symbols are:[evalfstart_4] 7.66/3.99 7.66/3.99 7.66/3.99 ---------------------------------------- 7.66/3.99 7.66/3.99 (1) Loat Proof (FINISHED) 7.66/3.99 7.66/3.99 7.66/3.99 ### Pre-processing the ITS problem ### 7.66/3.99 7.66/3.99 7.66/3.99 7.66/3.99 Initial linear ITS problem 7.66/3.99 7.66/3.99 Start location: evalfstart 7.66/3.99 7.66/3.99 0: evalfstart -> evalfentryin : [], cost: 1 7.66/3.99 7.66/3.99 1: evalfentryin -> evalfbb7in : A'=0, [], cost: 1 7.66/3.99 7.66/3.99 2: evalfbb7in -> evalfbb5in : C'=0, [ B^3>=0 && 0>=B^3 && 0>=1+A ], cost: 1 7.66/3.99 7.66/3.99 3: evalfbb7in -> evalfbb5in : C'=0, [ B^3>=1 && free>=0 && B^3>=2*free && 1+2*free>=B^3 && free>=1+A ], cost: 1 7.66/3.99 7.66/3.99 4: evalfbb7in -> evalfbb5in : C'=0, [ 0>=1+B^3 && 0>=free_1 && free_1>=1+A && 2*free_1>=B^3 && 1+B^3>=2*free_1 ], cost: 1 7.66/3.99 7.66/3.99 5: evalfbb7in -> evalfreturnin : [ B^3>=0 && 0>=B^3 && A>=0 ], cost: 1 7.66/3.99 7.66/3.99 6: evalfbb7in -> evalfreturnin : [ B^3>=1 && free_2>=0 && B^3>=2*free_2 && 1+2*free_2>=B^3 && A>=free_2 ], cost: 1 7.66/3.99 7.66/3.99 7: evalfbb7in -> evalfreturnin : [ 0>=1+B^3 && 0>=free_3 && A>=free_3 && 2*free_3>=B^3 && 1+B^3>=2*free_3 ], cost: 1 7.66/3.99 7.66/3.99 8: evalfbb5in -> evalfbb3in : D'=0, [ B>=1+C ], cost: 1 7.66/3.99 7.66/3.99 9: evalfbb5in -> evalfbb6in : [ C>=B ], cost: 1 7.66/3.99 7.66/3.99 10: evalfbb3in -> evalfbb2in : [ C>=1+D ], cost: 1 7.66/3.99 7.66/3.99 11: evalfbb3in -> evalfbb4in : [ D>=C ], cost: 1 7.66/3.99 7.66/3.99 12: evalfbb2in -> evalfbb3in : D'=1+D, [], cost: 1 7.66/3.99 7.66/3.99 13: evalfbb4in -> evalfbb5in : C'=1+C, [], cost: 1 7.66/3.99 7.66/3.99 14: evalfbb6in -> evalfbb7in : A'=1+A, [], cost: 1 7.66/3.99 7.66/3.99 15: evalfreturnin -> evalfstop : [], cost: 1 7.66/3.99 7.66/3.99 7.66/3.99 7.66/3.99 Removed unreachable and leaf rules: 7.66/3.99 7.66/3.99 Start location: evalfstart 7.66/3.99 7.66/3.99 0: evalfstart -> evalfentryin : [], cost: 1 7.66/3.99 7.66/3.99 1: evalfentryin -> evalfbb7in : A'=0, [], cost: 1 7.66/3.99 7.66/3.99 2: evalfbb7in -> evalfbb5in : C'=0, [ B^3>=0 && 0>=B^3 && 0>=1+A ], cost: 1 7.66/3.99 7.66/3.99 3: evalfbb7in -> evalfbb5in : C'=0, [ B^3>=1 && free>=0 && B^3>=2*free && 1+2*free>=B^3 && free>=1+A ], cost: 1 7.66/3.99 7.66/3.99 4: evalfbb7in -> evalfbb5in : C'=0, [ 0>=1+B^3 && 0>=free_1 && free_1>=1+A && 2*free_1>=B^3 && 1+B^3>=2*free_1 ], cost: 1 7.66/3.99 7.66/3.99 8: evalfbb5in -> evalfbb3in : D'=0, [ B>=1+C ], cost: 1 7.66/3.99
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