details

property	value
status	complete
benchmark	#3.54.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	AG01

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.07145 seconds
cpu usage	4.72035
user time	4.51862
system time	0.201731
max virtual memory	1.8475476E7
max residence set size	298336.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 43 ms] (2) QTRS (3) Overlay + Local Confluence [EQUIVALENT, 0 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 0 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 0 ms] (8) QDP (9) PisEmptyProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(g(x)) -> g(f(f(x))) f(h(x)) -> h(g(x)) f'(s(x), y, y) -> f'(y, x, s(x)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(f(x_1)) = x_1 POL(f'(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + x_3 POL(g(x_1)) = x_1 POL(h(x_1)) = 2*x_1 POL(s(x_1)) = 1 + 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f'(s(x), y, y) -> f'(y, x, s(x)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(g(x)) -> g(f(f(x))) f(h(x)) -> h(g(x)) Q is empty. ---------------------------------------- (3) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(g(x)) -> g(f(f(x))) f(h(x)) -> h(g(x)) The set Q consists of the following terms: f(g(x0)) f(h(x0)) ---------------------------------------- (5) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: F(g(x)) -> F(f(x)) F(g(x)) -> F(x) The TRS R consists of the following rules: f(g(x)) -> g(f(f(x))) popout

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all output return to TRS Standard