details

property	value
status	complete
benchmark	aprove07.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	Secret_06_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	6.08122 seconds
cpu usage	20.8521
user time	19.8772
system time	0.974893
max virtual memory	3.7510204E7
max residence set size	3014504.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 33 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] (9) YES (10) QDP (11) MNOCProof [EQUIVALENT, 0 ms] (12) QDP (13) UsableRulesProof [EQUIVALENT, 0 ms] (14) QDP (15) QDPOrderProof [EQUIVALENT, 390 ms] (16) QDP (17) DependencyGraphProof [EQUIVALENT, 0 ms] (18) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: foo(0(x1)) -> 0(s(p(p(p(s(s(s(p(s(x1)))))))))) foo(s(x1)) -> p(s(p(p(p(s(s(p(s(s(p(s(foo(p(p(s(s(p(s(bar(p(p(s(s(p(s(x1)))))))))))))))))))))))))) bar(0(x1)) -> 0(p(s(s(s(x1))))) bar(s(x1)) -> p(s(p(p(s(s(foo(s(p(p(s(s(x1)))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(x1))))) Q is empty. ---------------------------------------- (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: FOO(0(x1)) -> P(p(p(s(s(s(p(s(x1)))))))) FOO(0(x1)) -> P(p(s(s(s(p(s(x1))))))) FOO(0(x1)) -> P(s(s(s(p(s(x1)))))) FOO(0(x1)) -> P(s(x1)) FOO(s(x1)) -> P(s(p(p(p(s(s(p(s(s(p(s(foo(p(p(s(s(p(s(bar(p(p(s(s(p(s(x1)))))))))))))))))))))))))) FOO(s(x1)) -> P(p(p(s(s(p(s(s(p(s(foo(p(p(s(s(p(s(bar(p(p(s(s(p(s(x1)))))))))))))))))))))))) FOO(s(x1)) -> P(p(s(s(p(s(s(p(s(foo(p(p(s(s(p(s(bar(p(p(s(s(p(s(x1))))))))))))))))))))))) FOO(s(x1)) -> P(s(s(p(s(s(p(s(foo(p(p(s(s(p(s(bar(p(p(s(s(p(s(x1)))))))))))))))))))))) FOO(s(x1)) -> P(s(s(p(s(foo(p(p(s(s(p(s(bar(p(p(s(s(p(s(x1))))))))))))))))))) FOO(s(x1)) -> P(s(foo(p(p(s(s(p(s(bar(p(p(s(s(p(s(x1)))))))))))))))) FOO(s(x1)) -> FOO(p(p(s(s(p(s(bar(p(p(s(s(p(s(x1)))))))))))))) FOO(s(x1)) -> P(p(s(s(p(s(bar(p(p(s(s(p(s(x1))))))))))))) FOO(s(x1)) -> P(s(s(p(s(bar(p(p(s(s(p(s(x1)))))))))))) FOO(s(x1)) -> P(s(bar(p(p(s(s(p(s(x1))))))))) FOO(s(x1)) -> BAR(p(p(s(s(p(s(x1))))))) FOO(s(x1)) -> P(p(s(s(p(s(x1)))))) FOO(s(x1)) -> P(s(s(p(s(x1))))) FOO(s(x1)) -> P(s(x1)) BAR(0(x1)) -> P(s(s(s(x1)))) BAR(s(x1)) -> P(s(p(p(s(s(foo(s(p(p(s(s(x1)))))))))))) BAR(s(x1)) -> P(p(s(s(foo(s(p(p(s(s(x1)))))))))) BAR(s(x1)) -> P(s(s(foo(s(p(p(s(s(x1))))))))) BAR(s(x1)) -> FOO(s(p(p(s(s(x1)))))) BAR(s(x1)) -> P(p(s(s(x1)))) BAR(s(x1)) -> P(s(s(x1))) P(p(s(x1))) -> P(x1) The TRS R consists of the following rules: foo(0(x1)) -> 0(s(p(p(p(s(s(s(p(s(x1)))))))))) foo(s(x1)) -> p(s(p(p(p(s(s(p(s(s(p(s(foo(p(p(s(s(p(s(bar(p(p(s(s(p(s(x1)))))))))))))))))))))))))) bar(0(x1)) -> 0(p(s(s(s(x1))))) bar(s(x1)) -> p(s(p(p(s(s(foo(s(p(p(s(s(x1)))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(x1))))) Q is empty. 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 22 less nodes. ---------------------------------------- popout

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