details

property	value
status	complete
benchmark	t007.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n178.star.cs.uiowa.edu
space	HirokawaMiddeldorp_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.61225 seconds
cpu usage	7.28761
user time	6.97448
system time	0.313124
max virtual memory	1.8875316E7
max residence set size	839576.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) FlatCCProof [EQUIVALENT, 0 ms] (2) QTRS (3) RootLabelingProof [EQUIVALENT, 0 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 9 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(a) -> f(b) g(b) -> g(a) f(x) -> g(x) Q is empty. ---------------------------------------- (1) FlatCCProof (EQUIVALENT) We used flat context closure [ROOTLAB] As Q is empty the flat context closure was sound AND complete. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(a) -> f(b) g(b) -> g(a) f(f(x)) -> f(g(x)) g(f(x)) -> g(g(x)) Q is empty. ---------------------------------------- (3) RootLabelingProof (EQUIVALENT) We used plain root labeling [ROOTLAB] with the following heuristic: LabelAll: All function symbols get labeled As Q is empty the root labeling was sound AND complete. ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f_{a}(a) -> f_{b}(b) g_{b}(b) -> g_{a}(a) f_{f_1}(f_{f_1}(x)) -> f_{g_1}(g_{f_1}(x)) f_{f_1}(f_{a}(x)) -> f_{g_1}(g_{a}(x)) f_{f_1}(f_{b}(x)) -> f_{g_1}(g_{b}(x)) f_{f_1}(f_{g_1}(x)) -> f_{g_1}(g_{g_1}(x)) g_{f_1}(f_{f_1}(x)) -> g_{g_1}(g_{f_1}(x)) g_{f_1}(f_{a}(x)) -> g_{g_1}(g_{a}(x)) g_{f_1}(f_{b}(x)) -> g_{g_1}(g_{b}(x)) g_{f_1}(f_{g_1}(x)) -> g_{g_1}(g_{g_1}(x)) Q is empty. ---------------------------------------- (5) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a) = 0 POL(b) = 1 POL(f_{a}(x_1)) = 2 + x_1 POL(f_{b}(x_1)) = x_1 POL(f_{f_1}(x_1)) = 1 + x_1 POL(f_{g_1}(x_1)) = x_1 POL(g_{a}(x_1)) = x_1 POL(g_{b}(x_1)) = x_1 POL(g_{f_1}(x_1)) = 1 + x_1 POL(g_{g_1}(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f_{a}(a) -> f_{b}(b) g_{b}(b) -> g_{a}(a) f_{f_1}(f_{f_1}(x)) -> f_{g_1}(g_{f_1}(x)) popout

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all output return to TRS Standard