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TRS Equat 89423 pair #381732672
details
property
value
status
complete
benchmark
AC05.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n094.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.45279717445 seconds
cpu usage
5.939344814
max memory
3.44809472E8
stage attributes
key
value
output-size
30887
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (2) EDP (3) EDependencyGraphProof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, 0 ms] (4) AND (5) EDP (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (7) EDP (8) EUsableRulesReductionPairsProof [EQUIVALENT, 8 ms] (9) EDP (10) EDPProblemToQDPProblemProof [EQUIVALENT, 0 ms] (11) QDP (12) MNOCProof [EQUIVALENT, 0 ms] (13) QDP (14) MRRProof [EQUIVALENT, 8 ms] (15) QDP (16) DependencyGraphProof [EQUIVALENT, 0 ms] (17) TRUE (18) EDP (19) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (20) EDP (21) EDPPoloProof [EQUIVALENT, 0 ms] (22) EDP (23) PisEmptyProof [EQUIVALENT, 0 ms] (24) YES (25) EDP (26) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (27) EDP (28) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (29) EDP (30) ERuleRemovalProof [EQUIVALENT, 8 ms] (31) EDP (32) EDPPoloProof [EQUIVALENT, 7 ms] (33) EDP (34) PisEmptyProof [EQUIVALENT, 0 ms] (35) YES (36) EDP (37) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (38) EDP (39) EDPPoloProof [EQUIVALENT, 0 ms] (40) EDP (41) EDPPoloProof [EQUIVALENT, 3 ms] (42) EDP (43) PisEmptyProof [EQUIVALENT, 0 ms] (44) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: p(s(x)) -> x 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(p(s(x)), p(s(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(p(s(x)), p(s(y))) MINUS(s(x), s(y)) -> P(s(x)) MINUS(s(x), s(y)) -> P(s(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)
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