details

property	value
status	complete
benchmark	aprove02.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	Secret_06_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	9.41479 seconds
cpu usage	32.6317
user time	30.6123
system time	2.01945
max virtual memory	4.0175836E7
max residence set size	4440004.0

stage attributes

key	value
starexec-result	YES

output

31.67/9.09 YES 32.38/9.25 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 32.38/9.25 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 32.38/9.25 32.38/9.25 32.38/9.25 Termination w.r.t. Q of the given QTRS could be proven: 32.38/9.25 32.38/9.25 (0) QTRS 32.38/9.25 (1) QTRSRRRProof [EQUIVALENT, 71 ms] 32.38/9.25 (2) QTRS 32.38/9.25 (3) DependencyPairsProof [EQUIVALENT, 28 ms] 32.38/9.25 (4) QDP 32.38/9.25 (5) DependencyGraphProof [EQUIVALENT, 3 ms] 32.38/9.25 (6) AND 32.38/9.25 (7) QDP 32.38/9.25 (8) UsableRulesProof [EQUIVALENT, 0 ms] 32.38/9.25 (9) QDP 32.38/9.25 (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] 32.38/9.25 (11) YES 32.38/9.25 (12) QDP 32.38/9.25 (13) MNOCProof [EQUIVALENT, 0 ms] 32.38/9.25 (14) QDP 32.38/9.25 (15) UsableRulesProof [EQUIVALENT, 0 ms] 32.38/9.25 (16) QDP 32.38/9.25 (17) QReductionProof [EQUIVALENT, 0 ms] 32.38/9.25 (18) QDP 32.38/9.25 (19) QDPOrderProof [EQUIVALENT, 18 ms] 32.38/9.25 (20) QDP 32.38/9.25 (21) DependencyGraphProof [EQUIVALENT, 0 ms] 32.38/9.25 (22) TRUE 32.38/9.25 32.38/9.25 32.38/9.25 ---------------------------------------- 32.38/9.25 32.38/9.25 (0) 32.38/9.25 Obligation: 32.38/9.25 Q restricted rewrite system: 32.38/9.25 The TRS R consists of the following rules: 32.38/9.25 32.38/9.25 v(s(x1)) -> s(p(p(s(s(s(s(s(s(s(s(w(p(p(s(s(p(s(p(s(x1)))))))))))))))))))) 32.38/9.25 v(0(x1)) -> p(p(s(s(0(p(p(s(s(s(s(s(x1)))))))))))) 32.38/9.25 w(s(x1)) -> s(s(s(s(s(s(p(p(s(s(v(p(p(s(s(s(p(p(s(s(x1)))))))))))))))))))) 32.38/9.25 w(0(x1)) -> p(s(p(p(p(p(p(p(p(p(s(s(0(s(s(s(s(s(s(x1))))))))))))))))))) 32.38/9.25 p(p(s(x1))) -> p(x1) 32.38/9.25 p(s(x1)) -> x1 32.38/9.25 p(0(x1)) -> 0(s(s(s(s(s(s(s(p(s(x1)))))))))) 32.38/9.25 32.38/9.25 Q is empty. 32.38/9.25 32.38/9.25 ---------------------------------------- 32.38/9.25 32.38/9.25 (1) QTRSRRRProof (EQUIVALENT) 32.38/9.25 Used ordering: 32.38/9.25 Polynomial interpretation [POLO]: 32.38/9.25 32.38/9.25 POL(0(x_1)) = x_1 32.38/9.25 POL(p(x_1)) = x_1 32.38/9.25 POL(s(x_1)) = x_1 32.38/9.25 POL(v(x_1)) = 1 + x_1 32.38/9.25 POL(w(x_1)) = 1 + x_1 32.38/9.25 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 32.38/9.25 32.38/9.25 v(0(x1)) -> p(p(s(s(0(p(p(s(s(s(s(s(x1)))))))))))) 32.38/9.25 w(0(x1)) -> p(s(p(p(p(p(p(p(p(p(s(s(0(s(s(s(s(s(s(x1))))))))))))))))))) 32.38/9.25 32.38/9.25 32.38/9.25 32.38/9.25 32.38/9.25 ---------------------------------------- 32.38/9.25 32.38/9.25 (2) 32.38/9.25 Obligation: 32.38/9.25 Q restricted rewrite system: 32.38/9.25 The TRS R consists of the following rules: 32.38/9.25 32.38/9.25 v(s(x1)) -> s(p(p(s(s(s(s(s(s(s(s(w(p(p(s(s(p(s(p(s(x1)))))))))))))))))))) 32.38/9.25 w(s(x1)) -> s(s(s(s(s(s(p(p(s(s(v(p(p(s(s(s(p(p(s(s(x1)))))))))))))))))))) 32.38/9.25 p(p(s(x1))) -> p(x1) 32.38/9.25 p(s(x1)) -> x1 32.38/9.25 p(0(x1)) -> 0(s(s(s(s(s(s(s(p(s(x1)))))))))) 32.38/9.25 32.38/9.25 Q is empty. 32.38/9.25 32.38/9.25 ---------------------------------------- 32.38/9.25 32.38/9.25 (3) DependencyPairsProof (EQUIVALENT) 32.38/9.25 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 32.38/9.25 ---------------------------------------- 32.38/9.25 32.38/9.25 (4) 32.38/9.25 Obligation: 32.38/9.25 Q DP problem: 32.38/9.25 The TRS P consists of the following rules: 32.38/9.25 32.38/9.25 V(s(x1)) -> P(p(s(s(s(s(s(s(s(s(w(p(p(s(s(p(s(p(s(x1))))))))))))))))))) 32.38/9.25 V(s(x1)) -> P(s(s(s(s(s(s(s(s(w(p(p(s(s(p(s(p(s(x1)))))))))))))))))) 32.38/9.25 V(s(x1)) -> W(p(p(s(s(p(s(p(s(x1))))))))) 32.38/9.25 V(s(x1)) -> P(p(s(s(p(s(p(s(x1)))))))) 32.38/9.25 V(s(x1)) -> P(s(s(p(s(p(s(x1))))))) 32.38/9.25 V(s(x1)) -> P(s(p(s(x1)))) popout

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all output return to SRS_Standard 2019-03-29 03.29