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TRS Equational pair #487523151
details
property
value
status
complete
benchmark
IJCAR_AC1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.39064192772 seconds
cpu usage
5.938946621
max memory
3.15850752E8
stage attributes
key
value
output-size
27705
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (2) EDP (3) EDependencyGraphProof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) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (7) EDP (8) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (9) EDP (10) ERuleRemovalProof [EQUIVALENT, 0 ms] (11) EDP (12) EDPPoloProof [EQUIVALENT, 9 ms] (13) EDP (14) PisEmptyProof [EQUIVALENT, 0 ms] (15) YES (16) EDP (17) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (18) EDP (19) EDPPoloProof [EQUIVALENT, 0 ms] (20) EDP (21) EDPPoloProof [EQUIVALENT, 23 ms] (22) EDP (23) PisEmptyProof [EQUIVALENT, 0 ms] (24) YES (25) EDP (26) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (27) EDP (28) EDPPoloProof [EQUIVALENT, 2 ms] (29) EDP (30) EDPPoloProof [EQUIVALENT, 0 ms] (31) EDP (32) PisEmptyProof [EQUIVALENT, 0 ms] (33) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: plus(x, 0) -> x plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) times(0, y) -> 0 times(s(0), y) -> y times(s(x), y) -> plus(y, times(x, y)) div(0, y) -> 0 div(x, y) -> quot(x, y, y) quot(0, s(y), z) -> 0 quot(s(x), s(y), z) -> quot(x, y, z) quot(x, 0, s(z)) -> s(div(x, s(z))) div(div(x, y), z) -> div(x, times(y, z)) The set E consists of the following equations: plus(x, y) == plus(y, x) times(x, y) == times(y, x) plus(plus(x, y), z) == plus(x, plus(y, z)) times(times(x, y), z) == times(x, times(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: PLUS(s(x), y) -> PLUS(x, y) TIMES(s(x), y) -> PLUS(y, times(x, y)) TIMES(s(x), y) -> TIMES(x, y) DIV(x, y) -> QUOT(x, y, y) QUOT(s(x), s(y), z) -> QUOT(x, y, z) QUOT(x, 0, s(z)) -> DIV(x, s(z)) DIV(div(x, y), z) -> DIV(x, times(y, z)) DIV(div(x, y), z) -> TIMES(y, z) PLUS(plus(s(x), y), ext) -> PLUS(s(plus(x, y)), ext) PLUS(plus(s(x), y), ext) -> PLUS(x, y) TIMES(times(0, y), ext) -> TIMES(0, ext) TIMES(times(s(x), y), ext) -> TIMES(plus(y, times(x, y)), ext) TIMES(times(s(x), y), ext) -> PLUS(y, times(x, y)) TIMES(times(s(x), y), ext) -> TIMES(x, y) The TRS R consists of the following rules:
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