details

property	value
status	complete
benchmark	4.06.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n174.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.15527 seconds
cpu usage	5.08283
user time	4.84778
system time	0.235049
max virtual memory	1.841096E7
max residence set size	322592.0

stage attributes

key	value
starexec-result	NO

output

NO 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be disproven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 22 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) TransformationProof [EQUIVALENT, 0 ms] (7) QDP (8) TransformationProof [EQUIVALENT, 0 ms] (9) QDP (10) TransformationProof [EQUIVALENT, 0 ms] (11) QDP (12) NonTerminationLoopProof [COMPLETE, 0 ms] (13) NO (14) QDP (15) QDPSizeChangeProof [EQUIVALENT, 0 ms] (16) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: *(*(x, y), z) -> *(x, *(y, z)) *(+(x, y), z) -> +(*(x, z), *(y, z)) *(x, +(y, f(z))) -> *(g(x, z), +(y, y)) 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: *^1(*(x, y), z) -> *^1(x, *(y, z)) *^1(*(x, y), z) -> *^1(y, z) *^1(+(x, y), z) -> *^1(x, z) *^1(+(x, y), z) -> *^1(y, z) *^1(x, +(y, f(z))) -> *^1(g(x, z), +(y, y)) The TRS R consists of the following rules: *(*(x, y), z) -> *(x, *(y, z)) *(+(x, y), z) -> +(*(x, z), *(y, z)) *(x, +(y, f(z))) -> *(g(x, z), +(y, y)) 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. ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Q DP problem: The TRS P consists of the following rules: *^1(x, +(y, f(z))) -> *^1(g(x, z), +(y, y)) The TRS R consists of the following rules: *(*(x, y), z) -> *(x, *(y, z)) *(+(x, y), z) -> +(*(x, z), *(y, z)) *(x, +(y, f(z))) -> *(g(x, z), +(y, y)) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (6) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule *^1(x, +(y, f(z))) -> *^1(g(x, z), +(y, y)) we obtained the following new rules [LPAR04]: (*^1(g(y_0, y_1), +(y_2, f(x2))) -> *^1(g(g(y_0, y_1), x2), +(y_2, y_2)),*^1(g(y_0, y_1), +(y_2, f(x2))) -> *^1(g(g(y_0, y_1), x2), +(y_2, y_2))) ---------------------------------------- popout

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