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TRS Standard pair #516965970
details
property
value
status
complete
benchmark
Ex4_4_Luc96b.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n090.star.cs.uiowa.edu
space
Strategy_removed_CSR_05
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
4.60929107666 seconds
cpu usage
6.419201926
max memory
4.89172992E8
stage attributes
key
value
output-size
4395
starexec-result
NO
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- NO proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be disproven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 18 ms] (6) QDP (7) UsableRulesProof [EQUIVALENT, 0 ms] (8) QDP (9) QReductionProof [EQUIVALENT, 0 ms] (10) QDP (11) NonTerminationLoopProof [COMPLETE, 0 ms] (12) NO ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(g(X), Y) -> f(X, f(g(X), Y)) 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(g(X), Y) -> f(X, f(g(X), Y)) The set Q consists of the following terms: f(g(x0), x1) ---------------------------------------- (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(g(X), Y) -> F(X, f(g(X), Y)) F(g(X), Y) -> F(g(X), Y) The TRS R consists of the following rules: f(g(X), Y) -> f(X, f(g(X), Y)) The set Q consists of the following terms: f(g(x0), x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. F(g(X), Y) -> F(X, f(g(X), Y)) The remaining pairs can at least be oriented weakly. Used ordering: Combined order from the following AFS and order. F(x1, x2) = x1 g(x1) = g(x1) Knuth-Bendix order [KBO] with precedence:trivial and weight map:
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