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Complexity_ITS 2019-03-21 04.46 pair #429991008
details
property
value
status
complete
benchmark
counterex1.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n072.star.cs.uiowa.edu
space
SAS10
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
16.6745 seconds
cpu usage
33.0989
user time
32.1809
system time
0.917985
max virtual memory
1.8836316E7
max residence set size
236000.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
33.00/16.64 WORST_CASE(Omega(n^1), ?) 33.00/16.65 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 33.00/16.65 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 33.00/16.65 33.00/16.65 33.00/16.65 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, INF). 33.00/16.65 33.00/16.65 (0) CpxIntTrs 33.00/16.65 (1) Loat Proof [FINISHED, 7984 ms] 33.00/16.65 (2) BOUNDS(n^1, INF) 33.00/16.65 33.00/16.65 33.00/16.65 ---------------------------------------- 33.00/16.65 33.00/16.65 (0) 33.00/16.65 Obligation: 33.00/16.65 Complexity Int TRS consisting of the following rules: 33.00/16.65 start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: 0 >= A + 1 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H 33.00/16.65 start(A, B, C, D, E, F, G, H) -> Com_1(lbl42(A, B - 1, C, D, E, F, G, H)) :|: A >= 0 && C >= 0 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H 33.00/16.65 start(A, B, C, D, E, F, G, H) -> Com_1(cut(A, B, C, D - 1, E, F, G, H)) :|: A >= 0 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H 33.00/16.65 start(A, B, C, D, E, F, G, H) -> Com_1(lbl72(A, 1 + B, C, D - 1, B, F, G, H)) :|: H >= C && A >= 0 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H 33.00/16.65 lbl72(A, B, C, D, E, F, G, H) -> Com_1(cut(A, B, C, D, E, F, G, H)) :|: A >= D + 1 && D + 1 >= 0 && H + 1 >= B && E + 1 >= B && E + 1 <= B && G >= H && G <= H 33.00/16.65 lbl72(A, B, C, D, E, F, G, H) -> Com_1(lbl72(A, 1 + B, C, D, B, F, G, H)) :|: H >= B && A >= D + 1 && D + 1 >= 0 && H + 1 >= B && E + 1 >= B && E + 1 <= B && G >= H && G <= H 33.00/16.65 lbl42(A, B, C, D, E, F, G, H) -> Com_1(lbl42(A, B - 1, C, D, E, F, G, H)) :|: B >= 0 && B + 1 >= 0 && D >= 0 && A >= D && G >= H && G <= H 33.00/16.65 lbl42(A, B, C, D, E, F, G, H) -> Com_1(cut(A, B, C, D - 1, E, F, G, H)) :|: B + 1 >= 0 && D >= 0 && A >= D && G >= H && G <= H 33.00/16.65 lbl42(A, B, C, D, E, F, G, H) -> Com_1(lbl72(A, 1 + B, C, D - 1, B, F, G, H)) :|: H >= B && B + 1 >= 0 && D >= 0 && A >= D && G >= H && G <= H 33.00/16.65 cut(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: A >= 0 && D + 1 >= 0 && D + 1 <= 0 && G >= H && G <= H 33.00/16.65 cut(A, B, C, D, E, F, G, H) -> Com_1(lbl42(A, B - 1, C, D, E, F, G, H)) :|: D >= 0 && B >= 0 && D + 1 >= 0 && A >= D + 1 && G >= H && G <= H 33.00/16.65 cut(A, B, C, D, E, F, G, H) -> Com_1(cut(A, B, C, D - 1, E, F, G, H)) :|: D >= 0 && D + 1 >= 0 && A >= D + 1 && G >= H && G <= H 33.00/16.65 cut(A, B, C, D, E, F, G, H) -> Com_1(lbl72(A, 1 + B, C, D - 1, B, F, G, H)) :|: H >= B && D >= 0 && D + 1 >= 0 && A >= D + 1 && G >= H && G <= H 33.00/16.65 start0(A, B, C, D, E, F, G, H) -> Com_1(start(A, C, C, A, F, F, H, H)) :|: TRUE 33.00/16.65 33.00/16.65 The start-symbols are:[start0_8] 33.00/16.65 33.00/16.65 33.00/16.65 ---------------------------------------- 33.00/16.65 33.00/16.65 (1) Loat Proof (FINISHED) 33.00/16.65 33.00/16.65 33.00/16.65 ### Pre-processing the ITS problem ### 33.00/16.65 33.00/16.65 33.00/16.65 33.00/16.65 Initial linear ITS problem 33.00/16.65 33.00/16.65 Start location: start0 33.00/16.65 33.00/16.65 0: start -> stop : [ 0>=1+A && B==C && D==A && E==F && G==H ], cost: 1 33.00/16.65 33.00/16.65 1: start -> lbl42 : B'=-1+B, [ A>=0 && C>=0 && B==C && D==A && E==F && G==H ], cost: 1 33.00/16.65 33.00/16.65 2: start -> cut : D'=-1+D, [ A>=0 && B==C && D==A && E==F && G==H ], cost: 1 33.00/16.65 33.00/16.65 3: start -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=C && A>=0 && B==C && D==A && E==F && G==H ], cost: 1 33.00/16.65 33.00/16.65 4: lbl72 -> cut : [ A>=1+D && 1+D>=0 && 1+H>=B && 1+E==B && G==H ], cost: 1 33.00/16.65 33.00/16.65 5: lbl72 -> lbl72 : B'=1+B, E'=B, [ H>=B && A>=1+D && 1+D>=0 && 1+H>=B && 1+E==B && G==H ], cost: 1 33.00/16.65 33.00/16.65 6: lbl42 -> lbl42 : B'=-1+B, [ B>=0 && 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1 33.00/16.65 33.00/16.65 7: lbl42 -> cut : D'=-1+D, [ 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1 33.00/16.65 33.00/16.65 8: lbl42 -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=B && 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1 33.00/16.65 33.00/16.65 9: cut -> stop : [ A>=0 && 1+D==0 && G==H ], cost: 1 33.00/16.65 33.00/16.65 10: cut -> lbl42 : B'=-1+B, [ D>=0 && B>=0 && 1+D>=0 && A>=1+D && G==H ], cost: 1 33.00/16.65 33.00/16.65 11: cut -> cut : D'=-1+D, [ D>=0 && 1+D>=0 && A>=1+D && G==H ], cost: 1 33.00/16.65 33.00/16.65 12: cut -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=B && D>=0 && 1+D>=0 && A>=1+D && G==H ], cost: 1 33.00/16.65 33.00/16.65 13: start0 -> start : B'=C, D'=A, E'=F, G'=H, [], cost: 1 33.00/16.65 33.00/16.65 33.00/16.65 33.00/16.65 Removed unreachable and leaf rules: 33.00/16.65 33.00/16.65 Start location: start0 33.00/16.65 33.00/16.65 1: start -> lbl42 : B'=-1+B, [ A>=0 && C>=0 && B==C && D==A && E==F && G==H ], cost: 1 33.00/16.65 33.00/16.65 2: start -> cut : D'=-1+D, [ A>=0 && B==C && D==A && E==F && G==H ], cost: 1 33.00/16.65 33.00/16.65 3: start -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=C && A>=0 && B==C && D==A && E==F && G==H ], cost: 1 33.00/16.65 33.00/16.65 4: lbl72 -> cut : [ A>=1+D && 1+D>=0 && 1+H>=B && 1+E==B && G==H ], cost: 1 33.00/16.65 33.00/16.65 5: lbl72 -> lbl72 : B'=1+B, E'=B, [ H>=B && A>=1+D && 1+D>=0 && 1+H>=B && 1+E==B && G==H ], cost: 1 33.00/16.65 33.00/16.65 6: lbl42 -> lbl42 : B'=-1+B, [ B>=0 && 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1 33.00/16.65 33.00/16.65 7: lbl42 -> cut : D'=-1+D, [ 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1 33.00/16.65 33.00/16.65 8: lbl42 -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=B && 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1 33.00/16.65 33.00/16.65 10: cut -> lbl42 : B'=-1+B, [ D>=0 && B>=0 && 1+D>=0 && A>=1+D && G==H ], cost: 1 33.00/16.65
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