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TRS Equational pair #487092740
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
n145.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.55504 seconds
cpu usage
5.96133
user time
5.7113
system time
0.250035
max virtual memory
1.8476724E7
max residence set size
350528.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (2) EDP (3) EDependencyGraphProof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, 8 ms] (9) EDP (10) EDPProblemToQDPProblemProof [EQUIVALENT, 0 ms] (11) QDP (12) MNOCProof [EQUIVALENT, 0 ms] (13) QDP (14) MRRProof [EQUIVALENT, 0 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, 21 ms] (29) EDP (30) ERuleRemovalProof [EQUIVALENT, 0 ms] (31) EDP (32) EDPPoloProof [EQUIVALENT, 0 ms] (33) EDP (34) PisEmptyProof [EQUIVALENT, 0 ms] (35) YES (36) EDP (37) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (38) EDP (39) EDPPoloProof [EQUIVALENT, 21 ms] (40) EDP (41) EDPPoloProof [EQUIVALENT, 0 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) 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)
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