details

property	value
status	complete
benchmark	ExIntrod_Zan97_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.857 seconds
cpu usage	1135.94
user time	1123.42
system time	12.5183
max virtual memory	3.7854544E7
max residence set size	1.5366964E7

stage attributes

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

output

WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 625 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: fact(X) -> if(zero(X), n__s(n__0), n__prod(X, n__fact(n__p(X)))) add(0, X) -> X add(s(X), Y) -> s(add(X, Y)) prod(0, X) -> 0 prod(s(X), Y) -> add(Y, prod(X, Y)) if(true, X, Y) -> activate(X) if(false, X, Y) -> activate(Y) zero(0) -> true zero(s(X)) -> false p(s(X)) -> X s(X) -> n__s(X) 0 -> n__0 prod(X1, X2) -> n__prod(X1, X2) fact(X) -> n__fact(X) p(X) -> n__p(X) activate(n__s(X)) -> s(activate(X)) activate(n__0) -> 0 activate(n__prod(X1, X2)) -> prod(activate(X1), activate(X2)) activate(n__fact(X)) -> fact(activate(X)) activate(n__p(X)) -> p(activate(X)) activate(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(n__s(x_1)) -> n__s(encArg(x_1)) encArg(n__0) -> n__0 encArg(n__prod(x_1, x_2)) -> n__prod(encArg(x_1), encArg(x_2)) encArg(n__fact(x_1)) -> n__fact(encArg(x_1)) encArg(n__p(x_1)) -> n__p(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_fact(x_1)) -> fact(encArg(x_1)) encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) encArg(cons_prod(x_1, x_2)) -> prod(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_zero(x_1)) -> zero(encArg(x_1)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_0) -> 0 encArg(cons_activate(x_1)) -> activate(encArg(x_1)) encode_fact(x_1) -> fact(encArg(x_1)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_zero(x_1) -> zero(encArg(x_1)) encode_n__s(x_1) -> n__s(encArg(x_1)) encode_n__0 -> n__0 encode_n__prod(x_1, x_2) -> n__prod(encArg(x_1), encArg(x_2)) encode_n__fact(x_1) -> n__fact(encArg(x_1)) encode_n__p(x_1) -> n__p(encArg(x_1)) encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_prod(x_1, x_2) -> prod(encArg(x_1), encArg(x_2)) encode_true -> true encode_activate(x_1) -> activate(encArg(x_1)) encode_false -> false encode_p(x_1) -> p(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). popout

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

job log

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actions

all output return to Derivational Complexity: TRS Innermost