details

property	value
status	complete
benchmark	4.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	MNZ_10

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.669 seconds
cpu usage	590.797
user time	585.477
system time	5.31991
max virtual memory	2.1581076E7
max residence set size	5073996.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 178 ms] (4) CpxRelTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (6) CdtProblem (7) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (8) CdtProblem (9) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CdtProblem (13) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (14) CdtProblem (15) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 59 ms] (18) CdtProblem (19) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (20) BOUNDS(1, 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: s(s(0)) -> f(s(0)) g(x) -> h(x, x) s(x) -> h(x, 0) s(x) -> h(0, x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x), g(x)) -> f(s(x)) s(0) -> k(0) s(k(0)) -> 0 s(s(s(0))) -> k(s(0)) k(s(0)) -> s(0) s(s(s(s(s(s(s(s(s(s(s(0))))))))))) -> k(s(s(0))) k(s(s(0))) -> s(s(s(s(s(s(s(s(s(0))))))))) h(k(x), g(x)) -> k(s(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(0) -> 0 encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_g(x_1)) -> g(encArg(x_1)) encArg(cons_f(x_1)) -> f(encArg(x_1)) encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) encArg(cons_k(x_1)) -> k(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0 encode_f(x_1) -> f(encArg(x_1)) encode_g(x_1) -> g(encArg(x_1)) encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2)) encode_k(x_1) -> k(encArg(x_1)) ---------------------------------------- (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: s(s(0)) -> f(s(0)) g(x) -> h(x, x) s(x) -> h(x, 0) s(x) -> h(0, x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x), g(x)) -> f(s(x)) s(0) -> k(0) s(k(0)) -> 0 s(s(s(0))) -> k(s(0)) k(s(0)) -> s(0) s(s(s(s(s(s(s(s(s(s(s(0))))))))))) -> k(s(s(0))) k(s(s(0))) -> s(s(s(s(s(s(s(s(s(0))))))))) h(k(x), g(x)) -> k(s(x)) The (relative) TRS S consists of the following rules: popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Derivational Complexity: TRS Innermost