details

property	value
status	complete
benchmark	test76.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n113.star.cs.uiowa.edu
space	Mixed_innermost

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	10.537678957 seconds
cpu usage	10.273275843
max memory	5.91060992E8

stage attributes

key	value
output-size	7025
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 18 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) QReductionProof [EQUIVALENT, 0 ms] (9) QDP (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] (11) YES (12) QDP (13) UsableRulesProof [EQUIVALENT, 0 ms] (14) QDP (15) QReductionProof [EQUIVALENT, 0 ms] (16) QDP (17) TransformationProof [EQUIVALENT, 0 ms] (18) QDP (19) DependencyGraphProof [EQUIVALENT, 0 ms] (20) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: +(X, 0) -> X +(X, s(Y)) -> s(+(X, Y)) f(0, s(0), X) -> f(X, +(X, X), X) g(X, Y) -> X g(X, Y) -> Y The set Q consists of the following terms: +(x0, 0) +(x0, s(x1)) f(0, s(0), x0) g(x0, x1) ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: +^1(X, s(Y)) -> +^1(X, Y) F(0, s(0), X) -> F(X, +(X, X), X) F(0, s(0), X) -> +^1(X, X) The TRS R consists of the following rules: +(X, 0) -> X +(X, s(Y)) -> s(+(X, Y)) f(0, s(0), X) -> f(X, +(X, X), X) g(X, Y) -> X g(X, Y) -> Y The set Q consists of the following terms: +(x0, 0) +(x0, s(x1)) f(0, s(0), x0) g(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node. ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) popout

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job log

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actions

all output return to TRS Innermost