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TRS Standard pair #487067783
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
n177.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.6656 seconds
cpu usage
6.72095
user time
6.44305
system time
0.2779
max virtual memory
1.8411188E7
max residence set size
387808.0
stage attributes
key
value
starexec-result
NO
output
NO proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be disproven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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, 121 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)) ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules:
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