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	n170.star.cs.uiowa.edu
space	HirokawaMiddeldorp_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.6409509182 seconds
cpu usage	7.389469635
max memory	7.48388352E8

stage attributes

key	value
output-size	2895
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) FlatCCProof [EQUIVALENT, 0 ms] (2) QTRS (3) RootLabelingProof [EQUIVALENT, 0 ms] (4) QTRS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: popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Standard