details

property	value
status	complete
benchmark	26.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n187.star.cs.uiowa.edu
space	Various_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.75556 seconds
cpu usage	3.75754
user time	3.57586
system time	0.18168
max virtual memory	1.8477524E7
max residence set size	248868.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 0 ms] (6) QDP (7) PisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(f(x)) -> f(g(f(x), x)) f(f(x)) -> f(h(f(x), f(x))) g(x, y) -> y h(x, x) -> g(x, 0) 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: F(f(x)) -> F(g(f(x), x)) F(f(x)) -> G(f(x), x) F(f(x)) -> F(h(f(x), f(x))) F(f(x)) -> H(f(x), f(x)) H(x, x) -> G(x, 0) The TRS R consists of the following rules: f(f(x)) -> f(g(f(x), x)) f(f(x)) -> f(h(f(x), f(x))) g(x, y) -> y h(x, x) -> g(x, 0) 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 1 SCC with 3 less nodes. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: F(f(x)) -> F(h(f(x), f(x))) F(f(x)) -> F(g(f(x), x)) The TRS R consists of the following rules: f(f(x)) -> f(g(f(x), x)) f(f(x)) -> f(h(f(x), f(x))) g(x, y) -> y h(x, x) -> g(x, 0) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. F(f(x)) -> F(h(f(x), f(x))) F(f(x)) -> F(g(f(x), x)) The remaining pairs can at least be oriented weakly. Used ordering: Combined order from the following AFS and order. F(x1) = x1 f(x1) = f(x1) h(x1, x2) = h g(x1, x2) = x2 popout

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all output return to TRS Standard