details

property	value
status	complete
benchmark	t010.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n190.star.cs.uiowa.edu
space	HirokawaMiddeldorp_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.85899 seconds
cpu usage	4.22056
user time	4.00507
system time	0.215484
max virtual memory	1.894268E7
max residence set size	375712.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) FlatCCProof [EQUIVALENT, 0 ms] (2) QTRS (3) RootLabelingProof [EQUIVALENT, 0 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 4 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: g(b) -> f(b) f(a) -> g(a) b -> a 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: g(g(b)) -> g(f(b)) f(g(b)) -> f(f(b)) g(f(a)) -> g(g(a)) f(f(a)) -> f(g(a)) g(b) -> g(a) f(b) -> f(a) 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: g_{g_1}(g_{b}(b)) -> g_{f_1}(f_{b}(b)) f_{g_1}(g_{b}(b)) -> f_{f_1}(f_{b}(b)) g_{f_1}(f_{a}(a)) -> g_{g_1}(g_{a}(a)) f_{f_1}(f_{a}(a)) -> f_{g_1}(g_{a}(a)) g_{b}(b) -> g_{a}(a) f_{b}(b) -> f_{a}(a) Q is empty. ---------------------------------------- (5) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a) = 0 POL(b) = 1 POL(f_{a}(x_1)) = 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)) = 2 + 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: g_{g_1}(g_{b}(b)) -> g_{f_1}(f_{b}(b)) f_{g_1}(g_{b}(b)) -> f_{f_1}(f_{b}(b)) g_{f_1}(f_{a}(a)) -> g_{g_1}(g_{a}(a)) f_{f_1}(f_{a}(a)) -> f_{g_1}(g_{a}(a)) g_{b}(b) -> g_{a}(a) popout

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actions

all output return to TRS Standard