details

property	value
status	complete
benchmark	aprove05.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	Secret_06_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.9637 seconds
cpu usage	12.5923
user time	11.9264
system time	0.665809
max virtual memory	2.0538836E7
max residence set size	1647768.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 70 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 50 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QDPSizeChangeProof [EQUIVALENT, 1 ms] (11) YES (12) QDP (13) MNOCProof [EQUIVALENT, 6 ms] (14) QDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) QDP (17) QReductionProof [EQUIVALENT, 1 ms] (18) QDP (19) QDPOrderProof [EQUIVALENT, 22 ms] (20) QDP (21) PisEmptyProof [EQUIVALENT, 0 ms] (22) YES (23) QDP (24) MNOCProof [EQUIVALENT, 0 ms] (25) QDP (26) UsableRulesProof [EQUIVALENT, 0 ms] (27) QDP (28) QReductionProof [EQUIVALENT, 0 ms] (29) QDP (30) QDPOrderProof [EQUIVALENT, 0 ms] (31) QDP (32) PisEmptyProof [EQUIVALENT, 0 ms] (33) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: twoto(0(x1)) -> p(p(s(s(s(p(p(p(s(s(s(0(p(p(s(s(x1)))))))))))))))) twoto(s(x1)) -> p(p(s(s(p(p(p(s(s(s(twice(p(p(s(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))) twice(0(x1)) -> p(s(p(s(0(s(p(s(s(s(s(p(s(x1))))))))))))) twice(s(x1)) -> s(p(p(p(p(s(s(s(s(s(twice(p(s(p(s(p(s(p(s(x1))))))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(p(s(x1))))))) 0(x1) -> x1 Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 1 + x_1 POL(p(x_1)) = x_1 POL(s(x_1)) = x_1 POL(twice(x_1)) = x_1 POL(twoto(x_1)) = 1 + x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: twoto(0(x1)) -> p(p(s(s(s(p(p(p(s(s(s(0(p(p(s(s(x1)))))))))))))))) 0(x1) -> x1 ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: twoto(s(x1)) -> p(p(s(s(p(p(p(s(s(s(twice(p(p(s(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))) twice(0(x1)) -> p(s(p(s(0(s(p(s(s(s(s(p(s(x1))))))))))))) twice(s(x1)) -> s(p(p(p(p(s(s(s(s(s(twice(p(s(p(s(p(s(p(s(x1))))))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(p(s(x1))))))) Q is empty. ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. popout

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all output return to SRS Standard