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SRS Stand 10685 pair #381720060
details
property
value
status
complete
benchmark
z078.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n023.star.cs.uiowa.edu
space
Zantema_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
5.42629694939 seconds
cpu usage
18.206731086
max memory
2.75462144E9
stage attributes
key
value
output-size
8648
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 11 ms] (2) QTRS (3) Overlay + Local Confluence [EQUIVALENT, 2 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 8 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 1 ms] (8) AND (9) QDP (10) UsableRulesProof [EQUIVALENT, 0 ms] (11) QDP (12) QReductionProof [EQUIVALENT, 0 ms] (13) QDP (14) QDPOrderProof [EQUIVALENT, 9 ms] (15) QDP (16) PisEmptyProof [EQUIVALENT, 0 ms] (17) YES (18) QDP (19) UsableRulesProof [EQUIVALENT, 0 ms] (20) QDP (21) QReductionProof [EQUIVALENT, 0 ms] (22) QDP (23) MRRProof [EQUIVALENT, 5 ms] (24) QDP (25) DependencyGraphProof [EQUIVALENT, 0 ms] (26) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(0(x1)) -> s(0(x1)) d(0(x1)) -> 0(x1) d(s(x1)) -> s(s(d(p(s(x1))))) f(s(x1)) -> d(f(p(s(x1)))) p(s(x1)) -> x1 Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(d(x_1)) = x_1 POL(f(x_1)) = 1 + x_1 POL(p(x_1)) = x_1 POL(s(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(0(x1)) -> s(0(x1)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: d(0(x1)) -> 0(x1) d(s(x1)) -> s(s(d(p(s(x1))))) f(s(x1)) -> d(f(p(s(x1)))) p(s(x1)) -> x1 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:
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