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TRS Stand 20472 pair #381713748
details
property
value
status
complete
benchmark
z03.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n023.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.79732203484 seconds
cpu usage
3.915273414
max memory
2.48049664E8
stage attributes
key
value
output-size
5040
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) RFCMatchBoundsDPProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(f, a(g, a(f, x))) -> a(f, a(g, a(g, a(f, x)))) a(g, a(f, a(g, x))) -> a(g, a(f, a(f, a(g, x)))) 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: A(f, a(g, a(f, x))) -> A(f, a(g, a(g, a(f, x)))) A(f, a(g, a(f, x))) -> A(g, a(g, a(f, x))) A(g, a(f, a(g, x))) -> A(g, a(f, a(f, a(g, x)))) A(g, a(f, a(g, x))) -> A(f, a(f, a(g, x))) The TRS R consists of the following rules: a(f, a(g, a(f, x))) -> a(f, a(g, a(g, a(f, x)))) a(g, a(f, a(g, x))) -> a(g, a(f, a(f, a(g, x)))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) UsableRulesReductionPairsProof (EQUIVALENT) First, we A-transformed [FROCOS05] the QDP-Problem. Then we obtain the following A-transformed DP problem. The pairs P are: f1(g(f(x))) -> f1(g(g(f(x)))) f1(g(f(x))) -> g1(g(f(x))) g1(f(g(x))) -> g1(f(f(g(x)))) g1(f(g(x))) -> f1(f(g(x))) and the Q and R are: Q restricted rewrite system: The TRS R consists of the following rules: g(f(g(x))) -> g(f(f(g(x)))) f(g(f(x))) -> f(g(g(f(x)))) Q is empty. By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well. No dependency pairs are removed. The following rules are removed from R: a(f, a(g, a(f, x))) -> a(f, a(g, a(g, a(f, x)))) a(g, a(f, a(g, x))) -> a(g, a(f, a(f, a(g, x)))) Used ordering: POLO with Polynomial interpretation [POLO]: POL(f(x_1)) = x_1 POL(f1(x_1)) = x_1 POL(g(x_1)) = x_1 POL(g1(x_1)) = x_1 ---------------------------------------- (4) Obligation: Q DP problem:
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