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TRS Stand 20472 pair #381712788
details
property
value
status
complete
benchmark
15.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n098.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.98835802078 seconds
cpu usage
8.81681536
max memory
1.06825728E9
stage attributes
key
value
output-size
4509
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 7 ms] (4) QTRS (5) Overlay + Local Confluence [EQUIVALENT, 0 ms] (6) QTRS (7) DependencyPairsProof [EQUIVALENT, 0 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) QDP (11) QDPOrderProof [EQUIVALENT, 13 ms] (12) QDP (13) PisEmptyProof [EQUIVALENT, 0 ms] (14) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(s(x)) -> s(s(f(p(s(x))))) f(0) -> 0 p(s(x)) -> x Q is empty. ---------------------------------------- (1) QTRS Reverse (EQUIVALENT) We applied the QTRS Reverse Processor [REVERSE]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: s(f(x)) -> s(p(f(s(s(x))))) 0'(f(x)) -> 0'(x) s(p(x)) -> x Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0'(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: 0'(f(x)) -> 0'(x) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: s(f(x)) -> s(p(f(s(s(x))))) s(p(x)) -> x Q is empty. ---------------------------------------- (5) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (6) Obligation: Q restricted rewrite system: The TRS R consists of the following rules:
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