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TRS Relat 75837 pair #381725002
details
property
value
status
complete
benchmark
rt2-5.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n008.star.cs.uiowa.edu
space
Relative_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.68933987617 seconds
cpu usage
3.915586475
max memory
2.94342656E8
stage attributes
key
value
output-size
3399
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) FlatCCProof [EQUIVALENT, 0 ms] (2) RelTRS (3) RootLabelingProof [EQUIVALENT, 0 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 20 ms] (6) RelTRS (7) RIsEmptyProof [EQUIVALENT, 2 ms] (8) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: f(f(x)) -> x The relative TRS consists of the following S rules: f(x) -> g(f(g(f(x)))) ---------------------------------------- (1) FlatCCProof (EQUIVALENT) We used flat context closure [ROOTLAB] ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: f(f(f(x))) -> f(x) g(f(f(x))) -> g(x) The relative TRS consists of the following S rules: f(f(x)) -> f(g(f(g(f(x))))) g(f(x)) -> g(g(f(g(f(x))))) ---------------------------------------- (3) RootLabelingProof (EQUIVALENT) We used plain root labeling [ROOTLAB] with the following heuristic: LabelAll: All function symbols get labeled ---------------------------------------- (4) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: f_{f_1}(f_{f_1}(f_{f_1}(x))) -> f_{f_1}(x) f_{f_1}(f_{f_1}(f_{g_1}(x))) -> f_{g_1}(x) g_{f_1}(f_{f_1}(f_{f_1}(x))) -> g_{f_1}(x) g_{f_1}(f_{f_1}(f_{g_1}(x))) -> g_{g_1}(x) The relative TRS consists of the following S rules: f_{f_1}(f_{f_1}(x)) -> f_{g_1}(g_{f_1}(f_{g_1}(g_{f_1}(f_{f_1}(x))))) f_{f_1}(f_{g_1}(x)) -> f_{g_1}(g_{f_1}(f_{g_1}(g_{f_1}(f_{g_1}(x))))) g_{f_1}(f_{f_1}(x)) -> g_{g_1}(g_{f_1}(f_{g_1}(g_{f_1}(f_{f_1}(x))))) g_{f_1}(f_{g_1}(x)) -> g_{g_1}(g_{f_1}(f_{g_1}(g_{f_1}(f_{g_1}(x))))) ---------------------------------------- (5) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Polynomial interpretation [POLO]: POL(f_{f_1}(x_1)) = 1 + x_1 POL(f_{g_1}(x_1)) = x_1 POL(g_{f_1}(x_1)) = x_1 POL(g_{g_1}(x_1)) = x_1 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: f_{f_1}(f_{f_1}(f_{f_1}(x))) -> f_{f_1}(x)
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