details

property	value
status	complete
benchmark	aprove08.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n067.star.cs.uiowa.edu
space	Secret_06_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	9.18992 seconds
cpu usage	32.0384
user time	30.387
system time	1.65145
max virtual memory	8.3741192E7
max residence set size	4257792.0

stage attributes

key	value
starexec-result	YES

output

30.90/8.88 YES 31.76/9.08 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 31.76/9.08 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 31.76/9.08 31.76/9.08 31.76/9.08 Termination w.r.t. Q of the given QTRS could be proven: 31.76/9.08 31.76/9.08 (0) QTRS 31.76/9.08 (1) QTRSRRRProof [EQUIVALENT, 70 ms] 31.76/9.08 (2) QTRS 31.76/9.08 (3) DependencyPairsProof [EQUIVALENT, 45 ms] 31.76/9.08 (4) QDP 31.76/9.08 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 31.76/9.08 (6) AND 31.76/9.08 (7) QDP 31.76/9.08 (8) UsableRulesProof [EQUIVALENT, 0 ms] 31.76/9.08 (9) QDP 31.76/9.08 (10) QDPSizeChangeProof [EQUIVALENT, 1 ms] 31.76/9.08 (11) YES 31.76/9.08 (12) QDP 31.76/9.08 (13) MNOCProof [EQUIVALENT, 6 ms] 31.76/9.08 (14) QDP 31.76/9.08 (15) UsableRulesProof [EQUIVALENT, 0 ms] 31.76/9.08 (16) QDP 31.76/9.08 (17) QReductionProof [EQUIVALENT, 0 ms] 31.76/9.08 (18) QDP 31.76/9.08 (19) QDPOrderProof [EQUIVALENT, 0 ms] 31.76/9.08 (20) QDP 31.76/9.08 (21) DependencyGraphProof [EQUIVALENT, 0 ms] 31.76/9.08 (22) TRUE 31.76/9.08 31.76/9.08 31.76/9.08 ---------------------------------------- 31.76/9.08 31.76/9.08 (0) 31.76/9.08 Obligation: 31.76/9.08 Q restricted rewrite system: 31.76/9.08 The TRS R consists of the following rules: 31.76/9.08 31.76/9.08 i(0(x1)) -> p(s(p(s(0(p(s(p(s(x1))))))))) 31.76/9.08 i(s(x1)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))))))) 31.76/9.08 j(0(x1)) -> p(s(p(p(s(s(0(p(s(p(s(x1))))))))))) 31.76/9.08 j(s(x1)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1))))))))))))) 31.76/9.08 p(p(s(x1))) -> p(x1) 31.76/9.08 p(s(x1)) -> x1 31.76/9.08 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) 31.76/9.08 31.76/9.08 Q is empty. 31.76/9.08 31.76/9.08 ---------------------------------------- 31.76/9.08 31.76/9.08 (1) QTRSRRRProof (EQUIVALENT) 31.76/9.08 Used ordering: 31.76/9.08 Polynomial interpretation [POLO]: 31.76/9.08 31.76/9.08 POL(0(x_1)) = x_1 31.76/9.08 POL(i(x_1)) = 1 + x_1 31.76/9.08 POL(j(x_1)) = 1 + x_1 31.76/9.08 POL(p(x_1)) = x_1 31.76/9.08 POL(s(x_1)) = x_1 31.76/9.08 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 31.76/9.08 31.76/9.08 i(0(x1)) -> p(s(p(s(0(p(s(p(s(x1))))))))) 31.76/9.08 j(0(x1)) -> p(s(p(p(s(s(0(p(s(p(s(x1))))))))))) 31.76/9.08 31.76/9.08 31.76/9.08 31.76/9.08 31.76/9.08 ---------------------------------------- 31.76/9.08 31.76/9.08 (2) 31.76/9.08 Obligation: 31.76/9.08 Q restricted rewrite system: 31.76/9.08 The TRS R consists of the following rules: 31.76/9.08 31.76/9.08 i(s(x1)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))))))) 31.76/9.08 j(s(x1)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1))))))))))))) 31.76/9.08 p(p(s(x1))) -> p(x1) 31.76/9.08 p(s(x1)) -> x1 31.76/9.08 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) 31.76/9.08 31.76/9.08 Q is empty. 31.76/9.08 31.76/9.08 ---------------------------------------- 31.76/9.08 31.76/9.08 (3) DependencyPairsProof (EQUIVALENT) 31.76/9.08 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 31.76/9.08 ---------------------------------------- 31.76/9.08 31.76/9.08 (4) 31.76/9.08 Obligation: 31.76/9.08 Q DP problem: 31.76/9.08 The TRS P consists of the following rules: 31.76/9.08 31.76/9.08 I(s(x1)) -> P(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))))))) 31.76/9.08 I(s(x1)) -> P(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))))) 31.76/9.08 I(s(x1)) -> J(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))) 31.76/9.08 I(s(x1)) -> P(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))) 31.76/9.08 I(s(x1)) -> P(s(p(p(p(p(s(s(s(s(x1)))))))))) 31.76/9.08 I(s(x1)) -> P(p(p(p(s(s(s(s(x1)))))))) popout

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all output return to SRS_Standard 2019-03-29 03.29