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Derivational Complexity: TRS pair #487103090
details
property
value
status
timeout (wallclock)
benchmark
211471.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
space
ICFP_2010
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
300.031 seconds
cpu usage
968.19
user time
961.25
system time
6.94
max virtual memory
1.899466E7
max residence set size
1420.0
stage attributes
unavailable
output
KILLED proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 67 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 505 ms] (12) BOUNDS(1, INF) (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (16) CpxTRS (17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (18) CpxRelTRS (19) RcToIrcProof [BOTH BOUNDS(ID, ID), 988 ms] (20) CpxRelTRS (21) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CpxWeightedTrs (23) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CpxWeightedTrs (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CpxTypedWeightedTrs (27) CompletionProof [UPPER BOUND(ID), 0 ms] (28) CpxTypedWeightedCompleteTrs (29) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxTypedWeightedCompleteTrs (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 3 ms] (32) CpxRNTS (33) SimplificationProof [BOTH BOUNDS(ID, ID), 13 ms] (34) CpxRNTS (35) CompletionProof [UPPER BOUND(ID), 0 ms] (36) CpxTypedWeightedCompleteTrs (37) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) CpxTrsToCdtProof [UPPER BOUND(ID), 128 ms] (40) CdtProblem (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (42) CdtProblem (43) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (48) CdtProblem (49) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 421 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 97 ms] (52) CdtProblem (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 71 ms] (56) CdtProblem (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 440 ms] (64) CdtProblem (65) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 10.5 s] (66) CdtProblem ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0(x1) -> 1(x1) 0(0(x1)) -> 0(x1) 3(4(5(x1))) -> 4(3(5(x1))) 2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))) -> 0(0(0(1(0(1(1(1(0(1(1(1(1(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 1(1(0(0(1(1(0(1(0(0(1(0(1(1(1(1(1(0(0(1(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(1(0(0(1(0(0(1(1(0(0(0(0(1(1(0(0(1(0(1(0(0(0(0(0(0(1(0(0(0(1(0(1(1(0(0(1(1(0(1(1(0(1(1(0(1(0(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(1(1(0(1(1(0(0(1(1(0(1(0(0(1(1(0(0(1(0(1(1(0(1(0(1(1(1(0(1(0(1(1(0(0(0(1(0(1(1(0(1(1(0(1(1(0(0(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1))
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