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TRS Standard pair #516966910
details
property
value
status
complete
benchmark
4.40.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n082.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
3.06787395477 seconds
cpu usage
8.911750102
max memory
5.8417152E8
stage attributes
key
value
output-size
6446
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be disproven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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) TransformationProof [EQUIVALENT, 0 ms] (6) QDP (7) TransformationProof [EQUIVALENT, 0 ms] (8) QDP (9) MNOCProof [EQUIVALENT, 0 ms] (10) QDP (11) NonTerminationLoopProof [COMPLETE, 76 ms] (12) NO ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(f(f(a, x), y), z) -> f(f(x, z), f(y, z)) f(f(b, x), y) -> x f(c, y) -> 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(f(f(a, x), y), z) -> f(f(x, z), f(y, z)) f(f(b, x), y) -> x f(c, y) -> y The set Q consists of the following terms: f(f(f(a, x0), x1), x2) f(f(b, x0), x1) f(c, x0) ---------------------------------------- (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(f(f(a, x), y), z) -> F(f(x, z), f(y, z)) F(f(f(a, x), y), z) -> F(x, z) F(f(f(a, x), y), z) -> F(y, z) The TRS R consists of the following rules: f(f(f(a, x), y), z) -> f(f(x, z), f(y, z)) f(f(b, x), y) -> x f(c, y) -> y The set Q consists of the following terms: f(f(f(a, x0), x1), x2) f(f(b, x0), x1) f(c, x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) TransformationProof (EQUIVALENT) By forward instantiating [JAR06] the rule F(f(f(a, x), y), z) -> F(x, z) we obtained the following new rules [LPAR04]: (F(f(f(a, f(f(a, y_0), y_1)), x1), x2) -> F(f(f(a, y_0), y_1), x2),F(f(f(a, f(f(a, y_0), y_1)), x1), x2) -> F(f(f(a, y_0), y_1), x2)) ----------------------------------------
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