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Derivational Complexity: TRS Innermost pair #487105484
details
property
value
status
complete
benchmark
07.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.556 seconds
cpu usage
316.595
user time
313.649
system time
2.9454
max virtual memory
1.9046548E7
max residence set size
5405052.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 160 ms] (4) CpxRelTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) InliningProof [UPPER BOUND(ID), 220 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 163 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 3 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 158 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 74 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 1184 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 1553 ms] (38) CpxRNTS (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 574 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 628 ms] (44) CpxRNTS (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 564 ms] (48) CpxRNTS (49) IntTrsBoundProof [UPPER BOUND(ID), 585 ms] (50) CpxRNTS (51) FinalProof [FINISHED, 0 ms] (52) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: f(x, y) -> h(x, y) f(x, y) -> h(y, x) h(x, x) -> x S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (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(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: f(x, y) -> h(x, y) f(x, y) -> h(y, x) h(x, x) -> x
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