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TRS Stand 20472 pair #381712445
details
property
value
status
complete
benchmark
jwteparla1.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
Waldmann_06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.68398189545 seconds
cpu usage
3.683548493
max memory
2.3097344E8
stage attributes
key
value
output-size
4783
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) TransformationProof [EQUIVALENT, 0 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) QDP (9) UsableRulesProof [EQUIVALENT, 0 ms] (10) QDP (11) TransformationProof [EQUIVALENT, 0 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(x, f(a, f(f(a, a), a))) -> f(f(a, x), x) Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(x, f(a, f(f(a, a), a))) -> f(f(a, x), x) The set Q consists of the following terms: f(x0, f(a, f(f(a, a), a))) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: F(x, f(a, f(f(a, a), a))) -> F(f(a, x), x) F(x, f(a, f(f(a, a), a))) -> F(a, x) The TRS R consists of the following rules: f(x, f(a, f(f(a, a), a))) -> f(f(a, x), x) The set Q consists of the following terms: f(x0, f(a, f(f(a, a), a))) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule F(x, f(a, f(f(a, a), a))) -> F(f(a, x), x) at position [] we obtained the following new rules [LPAR04]: (F(f(a, f(f(a, a), a)), f(a, f(f(a, a), a))) -> F(f(f(a, a), a), f(a, f(f(a, a), a))),F(f(a, f(f(a, a), a)), f(a, f(f(a, a), a))) -> F(f(f(a, a), a), f(a, f(f(a, a), a)))) ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: F(x, f(a, f(f(a, a), a))) -> F(a, x) F(f(a, f(f(a, a), a)), f(a, f(f(a, a), a))) -> F(f(f(a, a), a), f(a, f(f(a, a), a)))
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