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TRS Equat 89423 pair #381732798
details
property
value
status
complete
benchmark
AC04.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n085.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.34505105019 seconds
cpu usage
5.948145326
max memory
3.0795776E8
stage attributes
key
value
output-size
28145
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (2) EDP (3) EDependencyGraphProof [EQUIVALENT, 1 ms] (4) AND (5) EDP (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (7) EDP (8) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (9) EDP (10) PisEmptyProof [EQUIVALENT, 0 ms] (11) YES (12) EDP (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (14) EDP (15) EDPPoloProof [EQUIVALENT, 0 ms] (16) EDP (17) PisEmptyProof [EQUIVALENT, 0 ms] (18) YES (19) EDP (20) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (21) EDP (22) EUsableRulesReductionPairsProof [EQUIVALENT, 12 ms] (23) EDP (24) ERuleRemovalProof [EQUIVALENT, 0 ms] (25) EDP (26) EDPPoloProof [EQUIVALENT, 0 ms] (27) EDP (28) PisEmptyProof [EQUIVALENT, 0 ms] (29) YES (30) EDP (31) ESharpUsableEquationsProof [EQUIVALENT, 2 ms] (32) EDP (33) EDPPoloProof [EQUIVALENT, 0 ms] (34) EDP (35) EDPPoloProof [EQUIVALENT, 0 ms] (36) EDP (37) PisEmptyProof [EQUIVALENT, 0 ms] (38) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: plus(x, 0) -> x plus(x, s(y)) -> s(plus(x, y)) times(x, 0) -> 0 times(x, s(y)) -> plus(x, times(x, y)) minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) div(0, s(y)) -> 0 div(s(x), s(y)) -> s(div(minus(x, y), s(y))) 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(x, s(y)) -> PLUS(x, y) TIMES(x, s(y)) -> PLUS(x, times(x, y)) TIMES(x, s(y)) -> TIMES(x, y) MINUS(s(x), s(y)) -> MINUS(x, y) DIV(s(x), s(y)) -> DIV(minus(x, y), s(y)) DIV(s(x), s(y)) -> MINUS(x, y) PLUS(plus(x, s(y)), ext) -> PLUS(s(plus(x, y)), ext) PLUS(plus(x, s(y)), ext) -> PLUS(x, y) TIMES(times(x, 0), ext) -> TIMES(0, ext) TIMES(times(x, s(y)), ext) -> TIMES(plus(x, times(x, y)), ext) TIMES(times(x, s(y)), ext) -> PLUS(x, times(x, y)) TIMES(times(x, s(y)), ext) -> TIMES(x, y) The TRS R consists of the following rules: plus(x, 0) -> x
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