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TRS Standard pair #487068638
details
property
value
status
complete
benchmark
jw43.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n187.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.6709 seconds
cpu usage
3.58946
user time
3.42141
system time
0.16805
max virtual memory
1.840994E7
max residence set size
239712.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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) DependencyGraphProof [EQUIVALENT, 0 ms] (6) QDP (7) UsableRulesProof [EQUIVALENT, 0 ms] (8) QDP (9) MRRProof [EQUIVALENT, 0 ms] (10) QDP (11) PisEmptyProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(x, f(f(a, a), a)) -> f(f(a, f(a, a)), 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(f(a, a), a)) -> f(f(a, f(a, a)), x) The set Q consists of the following terms: f(x0, 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(f(a, a), a)) -> F(f(a, f(a, a)), x) F(x, f(f(a, a), a)) -> F(a, f(a, a)) The TRS R consists of the following rules: f(x, f(f(a, a), a)) -> f(f(a, f(a, a)), x) The set Q consists of the following terms: f(x0, f(f(a, a), a)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: F(x, f(f(a, a), a)) -> F(f(a, f(a, a)), x) The TRS R consists of the following rules: f(x, f(f(a, a), a)) -> f(f(a, f(a, a)), x) The set Q consists of the following terms: f(x0, f(f(a, a), a)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (7) UsableRulesProof (EQUIVALENT) As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.
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