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TRS Equational pair #516978206
details
property
value
status
complete
benchmark
AC41.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n009.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.61251306534 seconds
cpu usage
6.956722242
max memory
4.86248448E8
stage attributes
key
value
output-size
16387
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (2) EDP (3) EDependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) EDP (6) EUsableRulesReductionPairsProof [EQUIVALENT, 16 ms] (7) EDP (8) ERuleRemovalProof [EQUIVALENT, 0 ms] (9) EDP (10) EDPPoloProof [EQUIVALENT, 0 ms] (11) EDP (12) PisEmptyProof [EQUIVALENT, 0 ms] (13) YES (14) EDP (15) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (16) EDP (17) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (18) EDP (19) PisEmptyProof [EQUIVALENT, 0 ms] (20) YES (21) EDP (22) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (23) EDP (24) EDPPoloProof [EQUIVALENT, 3 ms] (25) EDP (26) PisEmptyProof [EQUIVALENT, 0 ms] (27) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) minus(minus(x, y), z) -> minus(x, plus(y, z)) quot(0, s(y)) -> 0 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) The set E consists of the following equations: plus(x, y) == plus(y, x) plus(plus(x, y), z) == plus(x, plus(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: MINUS(s(x), s(y)) -> MINUS(x, y) MINUS(minus(x, y), z) -> MINUS(x, plus(y, z)) MINUS(minus(x, y), z) -> PLUS(y, z) QUOT(s(x), s(y)) -> QUOT(minus(x, y), s(y)) QUOT(s(x), s(y)) -> MINUS(x, y) PLUS(s(x), y) -> PLUS(x, y) PLUS(plus(s(x), y), ext) -> PLUS(s(plus(x, y)), ext) PLUS(plus(s(x), y), ext) -> PLUS(x, y) The TRS R consists of the following rules: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) minus(minus(x, y), z) -> minus(x, plus(y, z)) quot(0, s(y)) -> 0 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) plus(plus(s(x), y), ext) -> plus(s(plus(x, y)), ext) The set E consists of the following equations: plus(x, y) == plus(y, x) plus(plus(x, y), z) == plus(x, plus(y, z)) The set E# consists of the following equations: PLUS(x, y) == PLUS(y, x) PLUS(plus(x, y), z) == PLUS(x, plus(y, z))
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