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TRS Standard pair #516963850
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
n081.star.cs.uiowa.edu
space
Waldmann_06
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.22158288956 seconds
cpu usage
5.639386557
max memory
4.77954048E8
stage attributes
key
value
output-size
4776
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) TransformationProof [EQUIVALENT, 1 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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