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TRS Equational pair #516978131
details
property
value
status
complete
benchmark
kusakari1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n003.star.cs.uiowa.edu
space
Mixed_AC
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
3.15509390831 seconds
cpu usage
8.152464097
max memory
5.33516288E8
stage attributes
key
value
output-size
5303
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (2) EDP (3) ERuleRemovalProof [EQUIVALENT, 0 ms] (4) EDP (5) EDPPoloProof [EQUIVALENT, 0 ms] (6) EDP (7) PisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: +(g(x), g(y)) -> g(+(g(a), +(x, y))) The set E consists of the following equations: +(x, y) == +(y, x) +(+(x, y), z) == +(x, +(y, z)) ---------------------------------------- (1) EquationalDependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,DA_STEIN] we result in the following initial EDP problem: The TRS P consists of the following rules: +^1(g(x), g(y)) -> +^1(g(a), +(x, y)) +^1(g(x), g(y)) -> +^1(x, y) +^1(+(g(x), g(y)), ext) -> +^1(g(+(g(a), +(x, y))), ext) +^1(+(g(x), g(y)), ext) -> +^1(g(a), +(x, y)) +^1(+(g(x), g(y)), ext) -> +^1(x, y) The TRS R consists of the following rules: +(g(x), g(y)) -> g(+(g(a), +(x, y))) +(+(g(x), g(y)), ext) -> +(g(+(g(a), +(x, y))), ext) The set E consists of the following equations: +(x, y) == +(y, x) +(+(x, y), z) == +(x, +(y, z)) The set E# consists of the following equations: +^1(x, y) == +^1(y, x) +^1(+(x, y), z) == +^1(x, +(y, z)) We have to consider all minimal (P,E#,R,E)-chains ---------------------------------------- (2) Obligation: The TRS P consists of the following rules: +^1(g(x), g(y)) -> +^1(g(a), +(x, y)) +^1(g(x), g(y)) -> +^1(x, y) +^1(+(g(x), g(y)), ext) -> +^1(g(+(g(a), +(x, y))), ext) +^1(+(g(x), g(y)), ext) -> +^1(g(a), +(x, y)) +^1(+(g(x), g(y)), ext) -> +^1(x, y) The TRS R consists of the following rules: +(g(x), g(y)) -> g(+(g(a), +(x, y))) +(+(g(x), g(y)), ext) -> +(g(+(g(a), +(x, y))), ext) The set E consists of the following equations: +(x, y) == +(y, x) +(+(x, y), z) == +(x, +(y, z)) The set E# consists of the following equations: +^1(x, y) == +^1(y, x) +^1(+(x, y), z) == +^1(x, +(y, z)) We have to consider all minimal (P,E#,R,E)-chains ---------------------------------------- (3) ERuleRemovalProof (EQUIVALENT) By using the rule removal processor [DA_STEIN] with the following polynomial ordering [POLO], at least one Dependency Pair or term rewrite system rule of this EDP problem can be strictly oriented.
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