details

property	value
status	complete
benchmark	4057.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.875 seconds
cpu usage	865.647
user time	857.764
system time	7.88264
max virtual memory	1.8961332E7
max residence set size	1.4890772E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 53 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 125 ms] (8) 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: 0(3(4(x1))) -> 3(1(2(1(2(1(1(3(5(4(x1)))))))))) 3(2(5(x1))) -> 2(2(5(3(3(2(2(1(1(2(x1)))))))))) 4(1(0(x1))) -> 1(2(0(2(4(4(4(4(4(4(x1)))))))))) 0(0(5(0(x1)))) -> 0(0(2(2(2(3(3(3(1(1(x1)))))))))) 0(3(2(0(x1)))) -> 3(4(1(2(3(2(4(0(1(1(x1)))))))))) 3(4(0(5(x1)))) -> 2(1(1(0(1(1(4(5(4(2(x1)))))))))) 4(5(5(4(x1)))) -> 1(3(0(4(1(4(2(2(2(2(x1)))))))))) 5(0(5(0(x1)))) -> 5(2(4(2(5(2(2(3(2(4(x1)))))))))) 0(3(4(3(4(x1))))) -> 2(1(0(4(2(3(5(3(3(4(x1)))))))))) 3(4(4(5(0(x1))))) -> 2(2(1(1(3(5(1(2(2(0(x1)))))))))) 4(3(0(0(2(x1))))) -> 2(1(1(0(1(1(0(0(2(1(x1)))))))))) 4(3(3(2(5(x1))))) -> 1(1(1(4(2(5(2(1(4(5(x1)))))))))) 4(5(1(5(4(x1))))) -> 1(3(5(5(2(1(1(5(2(2(x1)))))))))) 5(4(5(1(0(x1))))) -> 2(1(1(5(3(1(4(2(1(0(x1)))))))))) 5(5(1(3(5(x1))))) -> 1(1(4(1(1(4(2(0(2(2(x1)))))))))) 0(0(5(0(3(1(x1)))))) -> 0(0(4(1(1(4(5(2(3(1(x1)))))))))) 0(3(5(0(5(1(x1)))))) -> 5(1(2(5(2(2(3(2(4(0(x1)))))))))) 0(5(1(0(3(5(x1)))))) -> 2(1(3(2(2(5(1(1(3(5(x1)))))))))) 0(5(5(4(5(1(x1)))))) -> 5(5(2(0(1(1(1(2(0(1(x1)))))))))) 3(0(3(4(2(5(x1)))))) -> 1(1(5(5(5(1(2(2(2(2(x1)))))))))) 3(5(2(5(3(1(x1)))))) -> 3(0(1(1(4(1(4(0(1(1(x1)))))))))) 5(0(3(3(2(5(x1)))))) -> 2(0(1(3(0(4(3(5(1(1(x1)))))))))) 5(4(0(3(4(3(x1)))))) -> 5(3(1(4(3(2(2(1(4(3(x1)))))))))) 5(4(1(0(0(0(x1)))))) -> 3(5(2(2(1(2(2(4(3(2(x1)))))))))) 5(4(5(3(3(0(x1)))))) -> 5(0(4(3(0(1(1(1(3(0(x1)))))))))) 5(4(5(4(5(4(x1)))))) -> 1(0(0(3(0(1(1(2(1(4(x1)))))))))) 5(5(0(4(5(4(x1)))))) -> 5(3(4(4(3(5(1(1(2(5(x1)))))))))) 0(2(0(0(5(4(5(x1))))))) -> 0(2(1(2(1(4(0(4(4(5(x1)))))))))) 0(2(0(2(5(0(5(x1))))))) -> 2(5(3(1(0(4(2(5(1(1(x1)))))))))) 0(3(0(0(3(5(0(x1))))))) -> 0(3(2(4(2(2(2(5(2(0(x1)))))))))) 0(3(4(4(0(1(5(x1))))))) -> 2(4(2(4(0(4(3(2(1(2(x1)))))))))) 0(5(5(4(4(0(5(x1))))))) -> 2(1(1(5(0(5(0(4(4(5(x1)))))))))) 1(2(0(3(2(3(3(x1))))))) -> 1(2(4(3(3(5(4(1(1(3(x1)))))))))) 1(3(4(0(0(5(4(x1))))))) -> 1(0(4(2(0(4(4(5(2(4(x1)))))))))) 3(3(0(0(4(0(2(x1))))))) -> 4(1(1(5(0(1(2(5(5(1(x1)))))))))) 3(5(0(5(5(5(4(x1))))))) -> 2(4(4(4(5(4(1(3(3(2(x1)))))))))) 4(0(0(4(5(4(0(x1))))))) -> 4(3(1(2(1(3(4(0(3(1(x1)))))))))) 4(0(4(0(5(4(5(x1))))))) -> 1(5(1(5(5(1(5(5(1(1(x1)))))))))) 4(3(0(5(2(2(4(x1))))))) -> 1(2(4(1(2(0(0(4(1(4(x1)))))))))) 4(3(4(4(3(3(5(x1))))))) -> 2(3(5(3(5(1(4(5(3(5(x1)))))))))) 5(0(1(3(3(2(0(x1))))))) -> 5(2(1(3(5(1(5(1(1(1(x1)))))))))) 5(0(5(0(5(0(3(x1))))))) -> 0(1(5(0(1(2(3(4(4(3(x1)))))))))) 5(1(0(0(1(3(4(x1))))))) -> 5(5(3(2(4(1(2(3(3(4(x1)))))))))) 5(2(0(3(0(2(4(x1))))))) -> 0(2(3(5(5(1(2(0(1(4(x1)))))))))) 5(3(0(0(0(5(4(x1))))))) -> 5(1(1(5(3(2(4(4(0(0(x1)))))))))) 5(4(3(3(0(5(3(x1))))))) -> 5(1(1(3(5(4(3(5(1(3(x1)))))))))) 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(2(x_1)) -> 2(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). popout

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

job log

popout

actions

all output return to Derivational Complexity: TRS Innermost