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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313512
details
property
value
status
complete
benchmark
Ex4_Zan97_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n032.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.561 seconds
cpu usage
684.167
user time
679.259
system time
4.90787
max virtual memory
3.7986676E7
max residence set size
5917496.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
683.89/291.49 WORST_CASE(Omega(n^1), ?) 684.04/291.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 684.04/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 684.04/291.51 684.04/291.51 684.04/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, EXP). 684.04/291.51 684.04/291.51 (0) CpxTRS 684.04/291.51 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 684.04/291.51 (2) CpxWeightedTrs 684.04/291.51 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 684.04/291.51 (4) CpxTypedWeightedTrs 684.04/291.51 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 684.04/291.51 (6) CpxTypedWeightedCompleteTrs 684.04/291.51 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 684.04/291.51 (8) CpxTypedWeightedCompleteTrs 684.04/291.51 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 684.04/291.51 (10) CpxRNTS 684.04/291.51 (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 684.04/291.51 (12) CpxRNTS 684.04/291.51 (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 684.04/291.51 (14) CpxRNTS 684.04/291.51 (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 684.04/291.51 (16) CpxRNTS 684.04/291.51 (17) IntTrsBoundProof [UPPER BOUND(ID), 282 ms] 684.04/291.51 (18) CpxRNTS 684.04/291.51 (19) IntTrsBoundProof [UPPER BOUND(ID), 96 ms] 684.04/291.51 (20) CpxRNTS 684.04/291.51 (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 684.04/291.51 (22) CpxRNTS 684.04/291.51 (23) IntTrsBoundProof [UPPER BOUND(ID), 252 ms] 684.04/291.51 (24) CpxRNTS 684.04/291.51 (25) IntTrsBoundProof [UPPER BOUND(ID), 53 ms] 684.04/291.51 (26) CpxRNTS 684.04/291.51 (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 684.04/291.51 (28) CpxRNTS 684.04/291.51 (29) IntTrsBoundProof [UPPER BOUND(ID), 188 ms] 684.04/291.51 (30) CpxRNTS 684.04/291.51 (31) IntTrsBoundProof [UPPER BOUND(ID), 62 ms] 684.04/291.51 (32) CpxRNTS 684.04/291.51 (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 684.04/291.51 (34) CpxRNTS 684.04/291.51 (35) IntTrsBoundProof [UPPER BOUND(ID), 213 ms] 684.04/291.51 (36) CpxRNTS 684.04/291.51 (37) IntTrsBoundProof [UPPER BOUND(ID), 156 ms] 684.04/291.51 (38) CpxRNTS 684.04/291.51 (39) FinalProof [FINISHED, 0 ms] 684.04/291.51 (40) BOUNDS(1, EXP) 684.04/291.51 (41) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 684.04/291.51 (42) TRS for Loop Detection 684.04/291.51 (43) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 684.04/291.51 (44) BEST 684.04/291.51 (45) proven lower bound 684.04/291.51 (46) LowerBoundPropagationProof [FINISHED, 0 ms] 684.04/291.51 (47) BOUNDS(n^1, INF) 684.04/291.51 (48) TRS for Loop Detection 684.04/291.51 684.04/291.51 684.04/291.51 ---------------------------------------- 684.04/291.51 684.04/291.51 (0) 684.04/291.51 Obligation: 684.04/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, EXP). 684.04/291.51 684.04/291.51 684.04/291.51 The TRS R consists of the following rules: 684.04/291.51 684.04/291.51 f(X) -> cons(X, n__f(g(X))) 684.04/291.51 g(0) -> s(0) 684.04/291.51 g(s(X)) -> s(s(g(X))) 684.04/291.51 sel(0, cons(X, Y)) -> X 684.04/291.51 sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) 684.04/291.51 f(X) -> n__f(X) 684.04/291.51 activate(n__f(X)) -> f(X) 684.04/291.51 activate(X) -> X 684.04/291.51 684.04/291.51 S is empty. 684.04/291.51 Rewrite Strategy: INNERMOST 684.04/291.51 ---------------------------------------- 684.04/291.51 684.04/291.51 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 684.04/291.51 Transformed relative TRS to weighted TRS 684.04/291.51 ---------------------------------------- 684.04/291.51 684.04/291.51 (2) 684.04/291.51 Obligation: 684.04/291.51 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, EXP). 684.04/291.51 684.04/291.51 684.04/291.51 The TRS R consists of the following rules: 684.04/291.51 684.04/291.51 f(X) -> cons(X, n__f(g(X))) [1] 684.04/291.51 g(0) -> s(0) [1] 684.04/291.51 g(s(X)) -> s(s(g(X))) [1] 684.04/291.51 sel(0, cons(X, Y)) -> X [1] 684.04/291.51 sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) [1] 684.04/291.51 f(X) -> n__f(X) [1] 684.04/291.51 activate(n__f(X)) -> f(X) [1] 684.04/291.51 activate(X) -> X [1] 684.04/291.51
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