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TRS Standard pair #487073883
details
property
value
status
complete
benchmark
teparla1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n175.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.72063 seconds
cpu usage
3.72789
user time
3.55937
system time
0.168515
max virtual memory
1.8475476E7
max residence set size
242700.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) UsableRulesProof [EQUIVALENT, 0 ms] (6) QDP (7) TransformationProof [EQUIVALENT, 0 ms] (8) QDP (9) TransformationProof [EQUIVALENT, 0 ms] (10) QDP (11) DependencyGraphProof [EQUIVALENT, 0 ms] (12) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(f(y, z), f(x, f(a, x))) -> f(f(f(a, z), f(x, a)), f(a, y)) Q is empty. ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: F(f(y, z), f(x, f(a, x))) -> F(f(f(a, z), f(x, a)), f(a, y)) F(f(y, z), f(x, f(a, x))) -> F(f(a, z), f(x, a)) F(f(y, z), f(x, f(a, x))) -> F(a, z) F(f(y, z), f(x, f(a, x))) -> F(x, a) F(f(y, z), f(x, f(a, x))) -> F(a, y) The TRS R consists of the following rules: f(f(y, z), f(x, f(a, x))) -> f(f(f(a, z), f(x, a)), f(a, y)) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: F(f(y, z), f(x, f(a, x))) -> F(f(f(a, z), f(x, a)), f(a, y)) The TRS R consists of the following rules: f(f(y, z), f(x, f(a, x))) -> f(f(f(a, z), f(x, a)), f(a, y)) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) UsableRulesProof (EQUIVALENT) We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: F(f(y, z), f(x, f(a, x))) -> F(f(f(a, z), f(x, a)), f(a, y)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (7) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule F(f(y, z), f(x, f(a, x))) -> F(f(f(a, z), f(x, a)), f(a, y)) we obtained the following new rules [LPAR04]: (F(f(f(a, z1), f(z2, a)), f(a, f(a, a))) -> F(f(f(a, f(z2, a)), f(a, a)), f(a, f(a, z1))),F(f(f(a, z1), f(z2, a)), f(a, f(a, a))) -> F(f(f(a, f(z2, a)), f(a, a)), f(a, f(a, z1)))) ----------------------------------------
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