details

property	value
status	complete
benchmark	45970.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	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	296.682 seconds
cpu usage	1047.49
user time	1039.45
system time	8.03379
max virtual memory	1.9013344E7
max residence set size	1.5326292E7

stage attributes

key	value
starexec-result	WORST_CASE(?, O(n^1))

output

WORST_CASE(?, O(n^1)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 69 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 560 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(0(2(2(3(x1)))))) -> 0(2(2(1(0(3(x1)))))) 0(4(4(1(0(4(x1)))))) -> 0(4(4(4(0(1(x1)))))) 0(4(0(0(4(2(3(5(1(x1))))))))) -> 5(0(3(2(4(0(0(1(4(x1))))))))) 1(2(3(1(0(1(4(2(0(x1))))))))) -> 4(0(3(2(1(1(2(1(0(x1))))))))) 1(3(4(0(4(1(1(2(3(5(4(4(x1)))))))))))) -> 2(4(4(0(1(3(5(1(4(3(4(1(x1)))))))))))) 4(1(1(3(3(0(1(5(0(4(4(2(2(3(3(5(4(3(x1)))))))))))))))))) -> 4(0(4(2(4(3(1(3(4(3(5(1(2(0(3(5(1(3(x1)))))))))))))))))) 1(0(4(3(1(2(1(2(0(4(3(3(2(1(5(2(3(2(1(x1))))))))))))))))))) -> 1(4(2(1(1(4(1(0(3(0(5(3(1(3(2(2(3(2(2(x1))))))))))))))))))) 1(1(1(3(0(4(5(0(3(0(1(1(3(0(4(5(3(3(0(x1))))))))))))))))))) -> 4(5(0(3(3(4(1(0(0(1(1(1(3(1(0(3(5(3(0(x1))))))))))))))))))) 1(3(2(3(0(5(0(4(1(1(2(4(4(3(3(5(4(0(5(x1))))))))))))))))))) -> 4(2(1(2(5(3(4(1(1(3(0(0(3(3(4(0(5(4(5(x1))))))))))))))))))) 3(0(2(2(0(1(1(5(0(1(1(1(0(2(0(4(5(0(1(x1))))))))))))))))))) -> 5(1(2(1(4(0(0(3(0(1(0(0(1(0(1(2(5(1(2(x1))))))))))))))))))) 0(2(1(5(4(1(5(4(0(1(2(0(2(1(2(1(1(1(3(5(2(5(x1)))))))))))))))))))))) -> 2(1(1(3(5(4(2(5(0(5(2(1(1(1(2(1(4(0(2(0(5(1(x1)))))))))))))))))))))) 2(2(5(3(3(3(0(4(1(3(5(4(5(1(3(4(1(0(3(5(4(0(x1)))))))))))))))))))))) -> 0(1(5(3(4(1(3(5(3(3(1(3(4(5(3(4(4(0(2(2(5(0(x1)))))))))))))))))))))) 2(5(5(1(4(3(3(2(1(1(1(5(0(4(4(3(5(1(4(1(4(5(2(x1))))))))))))))))))))))) -> 3(4(5(1(4(4(5(2(1(5(5(5(0(1(2(1(1(1(3(4(3(4(2(x1))))))))))))))))))))))) 3(4(0(2(2(3(2(4(2(3(5(3(5(0(1(3(5(5(2(4(4(2(3(3(x1)))))))))))))))))))))))) -> 5(5(3(2(2(2(0(5(4(3(3(3(2(0(2(4(2(1(5(3(4(3(4(3(x1)))))))))))))))))))))))) 5(5(2(0(2(1(5(5(2(1(4(4(5(2(4(4(1(1(1(3(2(5(5(5(x1)))))))))))))))))))))))) -> 5(4(5(0(5(4(2(1(2(4(1(1(2(1(2(4(5(3(1(5(2(5(5(5(x1)))))))))))))))))))))))) 1(5(2(4(1(3(3(5(3(0(4(2(5(1(5(2(0(1(0(3(0(5(5(1(4(x1))))))))))))))))))))))))) -> 1(5(2(3(1(5(4(5(5(2(3(4(2(3(5(4(1(1(3(0(0(1(0(5(0(x1))))))))))))))))))))))))) 3(1(5(1(0(4(4(1(1(2(2(0(2(3(3(2(2(3(3(5(4(1(2(5(1(x1))))))))))))))))))))))))) -> 1(3(0(3(5(5(2(1(2(3(2(5(2(3(1(0(2(1(3(1(4(1(2(4(4(x1))))))))))))))))))))))))) 0(0(1(4(0(0(4(2(1(5(5(3(0(3(4(0(1(4(3(1(5(5(2(0(0(2(3(x1))))))))))))))))))))))))))) -> 0(0(5(4(1(2(4(2(1(5(4(2(0(5(0(0(0(3(4(1(3(5(3(0(1(0(3(x1))))))))))))))))))))))))))) 1(1(5(4(4(5(0(4(5(1(1(0(3(2(1(3(0(2(1(5(3(2(0(4(5(0(2(x1))))))))))))))))))))))))))) -> 2(3(4(0(1(5(0(5(1(1(2(0(3(4(1(3(0(4(1(5(2(5(0(4(2(5(1(x1))))))))))))))))))))))))))) 1(5(2(4(3(0(1(4(3(5(0(5(0(1(3(2(0(1(4(3(3(2(1(0(1(5(5(x1))))))))))))))))))))))))))) -> 1(5(1(4(1(0(0(3(5(5(0(0(3(0(1(1(4(5(3(2(3(1(2(4(2(5(3(x1))))))))))))))))))))))))))) 0(1(2(5(3(3(1(0(4(1(4(2(0(1(0(4(4(1(0(5(3(2(1(2(5(2(5(1(x1)))))))))))))))))))))))))))) -> 0(1(1(5(3(5(4(0(2(3(0(0(0(4(5(1(4(1(2(1(5(2(1(4(3(2(2(1(x1)))))))))))))))))))))))))))) 0(4(1(4(2(2(4(0(0(3(5(3(0(0(5(0(4(5(5(5(3(2(1(1(0(2(3(1(x1)))))))))))))))))))))))))))) -> 0(1(2(4(1(1(3(0(5(2(3(0(3(0(5(0(4(5(2(4(5(4(1(5(0(2(0(3(x1)))))))))))))))))))))))))))) 2(0(3(1(0(4(3(1(5(2(2(4(1(1(3(0(2(4(2(5(2(2(2(4(1(5(5(1(2(x1))))))))))))))))))))))))))))) -> 2(0(0(2(2(1(5(2(3(1(3(3(1(4(5(2(1(4(2(5(2(2(2(0(5(4(4(1(1(x1))))))))))))))))))))))))))))) 0(5(0(2(3(0(4(0(0(4(3(3(5(0(4(5(4(1(4(0(2(5(5(5(3(1(5(2(2(3(3(x1))))))))))))))))))))))))))))))) -> 2(3(5(3(5(0(4(0(0(0(3(3(4(0(4(1(4(5(3(4(2(5(5(5(5(2(0(0(2(1(3(x1))))))))))))))))))))))))))))))) 1(2(3(5(3(5(0(3(3(3(1(3(1(0(3(3(5(2(0(3(4(4(0(0(4(0(4(0(0(2(2(x1))))))))))))))))))))))))))))))) -> 1(3(3(5(0(5(5(3(4(1(2(3(3(0(0(4(2(1(0(0(0(3(2(3(4(0(3(0(4(3(2(x1))))))))))))))))))))))))))))))) 3(2(4(2(2(3(1(4(1(2(0(1(0(5(2(1(3(0(1(1(2(0(4(0(1(0(3(4(2(1(4(x1))))))))))))))))))))))))))))))) -> 0(2(1(2(1(4(1(3(1(2(4(5(0(0(2(1(1(4(1(3(4(0(1(0(2(3(3(2(0(2(4(x1))))))))))))))))))))))))))))))) 4(0(4(0(4(2(1(5(1(2(3(1(0(0(3(3(4(3(5(4(2(1(5(5(3(4(0(1(3(5(2(x1))))))))))))))))))))))))))))))) -> 4(0(4(3(1(2(3(4(2(5(3(2(0(5(1(3(4(1(0(3(5(1(2(4(1(3(0(4(0(5(5(x1))))))))))))))))))))))))))))))) 2(2(4(3(5(5(4(1(3(0(4(5(5(2(2(3(3(5(2(1(0(3(1(1(0(3(3(3(0(0(1(0(3(x1))))))))))))))))))))))))))))))))) -> 2(4(1(5(1(5(0(4(0(0(0(2(3(2(3(3(2(5(1(5(1(3(3(2(5(3(3(4(3(1(0(0(3(x1))))))))))))))))))))))))))))))))) 2(4(4(0(2(1(3(5(0(0(1(4(4(2(1(1(2(0(0(5(2(2(3(2(5(5(1(0(1(1(3(4(4(5(x1)))))))))))))))))))))))))))))))))) -> 2(4(3(0(5(0(1(1(1(0(2(1(1(2(2(2(4(0(0(4(5(2(4(3(5(5(0(4(1(1(3(4(2(5(x1)))))))))))))))))))))))))))))))))) 5(4(3(5(2(3(5(1(2(2(3(1(3(2(3(2(4(1(0(1(4(5(4(1(4(4(0(1(0(2(5(2(2(0(x1)))))))))))))))))))))))))))))))))) -> 5(4(1(5(2(2(5(3(4(0(5(0(4(2(3(0(0(3(4(5(2(1(4(2(3(4(1(1(2(1(1(2(2(3(x1)))))))))))))))))))))))))))))))))) 0(3(0(4(5(5(5(1(3(0(4(4(3(4(5(2(5(0(0(1(5(0(5(5(0(4(5(1(1(0(4(3(4(5(2(x1))))))))))))))))))))))))))))))))))) -> 0(3(0(0(1(5(5(1(3(4(4(1(4(0(4(5(5(4(2(2(5(5(5(5(0(0(0(1(3(4(5(3(4(5(0(x1))))))))))))))))))))))))))))))))))) 4(2(1(2(2(1(5(1(5(3(0(5(3(5(0(4(4(3(1(2(1(2(0(2(4(4(3(1(1(4(4(5(5(1(2(x1))))))))))))))))))))))))))))))))))) -> 4(1(5(2(2(0(5(3(0(2(2(2(1(5(3(4(1(2(1(5(3(1(0(3(4(4(4(1(1(4(4(5(5(2(1(x1))))))))))))))))))))))))))))))))))) 5(4(4(1(1(3(5(2(2(2(5(3(3(3(0(4(5(3(2(3(0(5(5(1(2(2(0(1(1(3(1(5(0(0(2(x1))))))))))))))))))))))))))))))))))) -> 3(4(5(1(0(2(3(2(3(2(0(3(5(3(1(4(5(2(2(2(0(1(5(5(2(1(1(4(5(3(5(0(0(1(3(x1))))))))))))))))))))))))))))))))))) 0(0(3(0(0(0(3(4(1(4(0(5(2(1(5(2(4(1(1(1(5(2(2(5(3(4(0(0(4(3(1(3(5(4(1(1(x1)))))))))))))))))))))))))))))))))))) -> 0(0(1(4(0(5(0(1(4(4(0(0(2(1(5(3(1(0(1(0(5(2(2(5(3(4(3(1(4(3(3(4(5(1(2(1(x1)))))))))))))))))))))))))))))))))))) 2(1(1(4(3(2(2(4(1(5(3(3(3(3(2(4(4(3(0(1(4(3(2(0(0(2(1(5(2(2(3(0(1(5(1(2(x1)))))))))))))))))))))))))))))))))))) -> 0(3(1(2(3(4(0(2(2(3(1(3(1(3(5(4(4(3(2(1(4(3(4(2(0(1(1(5(2(2(3(0(5(2(1(2(x1)))))))))))))))))))))))))))))))))))) 4(5(4(4(4(0(4(4(5(5(2(0(2(5(0(3(1(4(3(4(3(0(1(4(4(1(0(4(5(4(3(3(1(1(0(5(x1)))))))))))))))))))))))))))))))))))) -> 4(4(4(5(3(1(1(2(5(5(3(4(4(5(1(3(3(4(4(0(0(0(5(0(1(1(0(4(5(2(0(3(4(4(4(4(x1)))))))))))))))))))))))))))))))))))) 0(0(5(5(1(0(1(4(5(2(0(5(2(5(2(1(0(5(1(1(4(5(0(2(1(0(3(4(1(2(5(0(1(4(4(5(3(5(x1)))))))))))))))))))))))))))))))))))))) -> 0(3(4(5(1(0(0(5(1(0(0(5(4(5(0(1(2(5(5(4(4(1(0(2(1(3(2(2(1(0(5(1(5(1(4(5(2(5(x1)))))))))))))))))))))))))))))))))))))) 0(1(3(0(3(1(0(3(0(4(3(0(3(2(1(3(5(0(5(3(0(1(0(1(1(4(3(0(5(1(4(3(3(3(0(0(0(5(3(4(x1)))))))))))))))))))))))))))))))))))))))) -> 0(3(1(0(5(4(0(3(0(4(5(0(5(1(3(3(0(0(3(0(3(1(3(2(1(1(5(4(3(1(1(0(3(3(0(0(3(4(3(0(x1)))))))))))))))))))))))))))))))))))))))) 4(3(3(0(0(0(3(2(4(3(0(0(4(4(2(4(4(2(1(2(5(5(0(0(4(2(5(5(1(0(4(4(5(0(2(3(3(2(4(4(0(4(x1)))))))))))))))))))))))))))))))))))))))))) -> 4(2(2(4(0(0(3(2(5(3(4(5(4(0(0(4(0(2(1(0(5(5(2(4(3(3(5(4(1(0(4(4(0(0(4(3(3(2(2(4(0(4(x1)))))))))))))))))))))))))))))))))))))))))) 0(1(0(4(0(1(1(1(1(1(0(3(4(3(3(1(4(0(2(0(1(1(0(4(4(3(3(5(0(1(1(0(3(0(4(0(0(4(0(3(1(3(5(3(5(x1))))))))))))))))))))))))))))))))))))))))))))) -> 0(3(3(1(0(1(3(1(0(1(5(3(4(0(3(1(4(0(2(3(1(4(0(5(4(0(3(0(1(1(1(0(0(0(4(0(0(4(1(5(1(1(4(3(3(x1))))))))))))))))))))))))))))))))))))))))))))) 0(2(2(3(1(3(4(0(5(3(3(2(0(2(1(5(0(2(0(3(2(1(4(5(0(4(4(0(2(3(0(1(2(1(2(1(1(5(3(2(3(0(3(5(2(x1))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(5(0(3(4(2(5(0(3(2(1(2(1(3(0(1(0(3(4(0(4(4(0(2(2(0(2(3(3(3(2(1(3(1(1(5(2(1(3(5(0(5(2(x1))))))))))))))))))))))))))))))))))))))))))))) 2(2(0(4(5(5(3(5(1(2(3(5(2(5(5(3(3(2(1(1(1(3(1(3(5(3(4(1(5(2(1(1(4(1(1(2(2(3(2(4(2(2(5(3(3(x1))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(1(5(1(3(2(1(3(1(3(2(5(5(3(5(5(1(2(1(3(5(3(1(2(4(0(3(5(4(2(4(1(1(2(2(3(3(2(2(4(5(5(3(x1))))))))))))))))))))))))))))))))))))))))))))) 2(5(0(5(0(1(5(1(3(4(4(3(1(3(3(3(0(5(3(3(0(4(3(3(3(2(4(4(2(2(5(2(4(3(3(5(1(2(1(0(4(1(5(2(3(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(0(5(0(2(5(1(3(3(2(3(1(4(3(2(0(5(3(3(4(4(3(2(3(2(4(1(0(4(5(2(4(3(0(5(1(1(2(3(4(1(5(3(3(5(3(x1))))))))))))))))))))))))))))))))))))))))))))))) 4(5(4(2(3(3(2(4(1(0(3(4(4(3(1(4(0(0(1(4(4(4(5(2(0(4(2(2(2(2(0(4(3(4(3(0(3(2(5(3(3(0(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 4(5(3(2(5(4(2(3(1(4(4(4(4(3(2(4(4(0(1(4(4(2(0(0(3(4(3(2(0(2(0(1(3(4(3(0(3(5(2(3(2(0(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))) 0(3(1(4(5(1(2(2(4(5(1(3(5(3(2(3(0(4(5(2(1(4(4(5(3(1(0(1(1(2(5(3(4(5(5(0(2(3(0(4(1(0(3(3(0(2(4(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 0(3(1(4(5(1(5(2(2(5(2(3(4(4(4(3(0(5(4(2(2(3(4(0(5(1(0(0(1(2(1(3(5(5(2(0(5(3(1(4(1(0(3(3(4(1(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(4(4(2(5(4(5(2(1(4(4(2(0(2(3(5(0(3(3(5(0(3(5(0(4(0(0(5(5(2(5(0(4(0(3(2(2(1(5(3(2(4(3(1(5(4(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 4(2(1(2(0(4(5(5(5(4(4(5(0(0(3(4(0(2(3(4(3(3(1(2(4(5(4(5(2(5(2(0(5(0(3(0(0(1(5(3(2(1(2(1(5(4(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) 2(3(1(5(1(2(3(3(3(5(2(1(5(5(3(4(0(5(2(2(2(3(2(3(3(3(3(1(3(2(2(0(2(1(4(1(4(4(3(2(4(4(0(4(2(4(3(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 1(3(2(3(3(2(3(4(2(4(2(0(1(5(3(4(0(5(2(2(1(3(2(1(5(3(3(3(3(2(2(0(2(2(4(4(3(1(5(3(0(4(5(4(2(3(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) 4(5(5(4(4(4(3(3(2(0(1(4(5(3(1(1(5(4(3(0(2(4(2(5(4(2(0(3(4(1(4(2(5(1(5(4(0(4(0(0(2(2(2(0(3(0(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 4(0(5(4(4(5(3(1(2(1(3(4(5(3(3(1(2(4(3(1(4(2(5(4(4(4(0(4(0(0(4(2(0(1(5(2(2(2(0(0(5(2(2(0(3(5(4(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(3(5(2(5(4(0(1(4(5(5(2(1(2(5(4(1(3(1(3(5(3(4(2(5(0(1(3(5(3(3(0(2(2(2(2(5(1(4(5(3(1(4(0(2(1(5(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(3(5(2(5(4(0(5(5(5(4(2(1(3(3(0(1(1(2(3(5(1(4(2(1(5(1(4(0(2(3(0(3(2(2(3(5(1(1(5(3(1(1(4(2(4(5(1(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) 4(0(3(4(1(4(0(4(5(3(0(2(3(4(2(0(5(2(4(1(5(3(0(4(2(5(3(5(1(0(1(1(0(3(5(3(3(4(5(0(4(4(3(3(2(1(1(5(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(1(0(4(5(1(0(4(5(3(0(2(3(4(2(0(5(2(4(1(0(3(0(1(1(5(0(3(1(1(4(3(5(2(5(2(5(4(4(3(5(4(3(3(3(4(0(3(5(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(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) ---------------------------------------- popout

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

job log

popout

actions

all output return to Derivational Complexity: TRS