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TRS Equational pair #487092791
details
property
value
status
complete
benchmark
RENAMED-BOOL_nokinds.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
Mixed_AC
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
15.6285 seconds
cpu usage
32.7116
user time
31.3898
system time
1.3218
max virtual memory
1.834614E7
max residence set size
3403564.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 34 ms] (2) EDP (3) EDependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) EDP (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (7) EDP (8) EUsableRulesReductionPairsProof [EQUIVALENT, 7 ms] (9) EDP (10) PisEmptyProof [EQUIVALENT, 0 ms] (11) YES (12) EDP (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (14) EDP (15) EDPPoloProof [EQUIVALENT, 30 ms] (16) EDP (17) EDPPoloProof [EQUIVALENT, 0 ms] (18) EDP (19) PisEmptyProof [EQUIVALENT, 0 ms] (20) YES (21) EDP (22) ESharpUsableEquationsProof [EQUIVALENT, 5 ms] (23) EDP (24) EDPPoloProof [EQUIVALENT, 955 ms] (25) EDP (26) EDependencyGraphProof [EQUIVALENT, 0 ms] (27) EDP (28) EDPPoloProof [EQUIVALENT, 1752 ms] (29) EDP (30) EDPPoloProof [EQUIVALENT, 2011 ms] (31) EDP (32) EDPPoloProof [EQUIVALENT, 1844 ms] (33) EDP (34) PisEmptyProof [EQUIVALENT, 0 ms] (35) YES (36) EDP (37) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (38) EDP (39) EDPPoloProof [EQUIVALENT, 1948 ms] (40) EDP (41) PisEmptyProof [EQUIVALENT, 0 ms] (42) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: U101(tt, A, B) -> _xor_(_and_(A, B), _xor_(A, B)) U11(tt, A) -> A U111(tt) -> false U121(tt, A) -> A U131(tt, B, U') -> U132(equal(_isNotEqualTo_(B, true), true), U') U132(tt, U') -> U' U141(tt, U) -> U U151(tt, A) -> _xor_(A, true) U21(tt, A, B, C) -> _xor_(_and_(A, B), _and_(A, C)) U31(tt) -> false U41(tt, A) -> A U51(tt, A, B) -> not_(_xor_(A, _and_(A, B))) U61(tt, U', U) -> U62(equal(_isNotEqualTo_(U, U'), true)) U62(tt) -> false U71(tt) -> true U81(tt, U', U) -> if_then_else_fi(_isEqualTo_(U, U'), false, true) U91(tt) -> false _and_(A, A) -> U11(isBool(A), A) _and_(A, _xor_(B, C)) -> U21(and(isBool(A), and(isBool(B), isBool(C))), A, B, C) _and_(false, A) -> U31(isBool(A)) _and_(true, A) -> U41(isBool(A), A) _implies_(A, B) -> U51(and(isBool(A), isBool(B)), A, B) _isEqualTo_(U, U') -> U61(and(isS(U'), isS(U)), U', U) _isEqualTo_(U, U) -> U71(isS(U)) _isNotEqualTo_(U, U') -> U81(and(isS(U'), isS(U)), U', U) _isNotEqualTo_(U, U) -> U91(isS(U)) _or_(A, B) -> U101(and(isBool(A), isBool(B)), A, B) _xor_(A, A) -> U111(isBool(A)) _xor_(false, A) -> U121(isBool(A), A) and(tt, X) -> X equal(X, X) -> tt if_then_else_fi(B, U, U') -> U131(and(isBool(B), and(isS(U'), isS(U))), B, U') if_then_else_fi(true, U, U') -> U141(and(isS(U'), isS(U)), U) isBool(false) -> tt isBool(true) -> tt isBool(_and_(V1, V2)) -> and(isBool(V1), isBool(V2)) isBool(_implies_(V1, V2)) -> and(isBool(V1), isBool(V2)) isBool(_isEqualTo_(V1, V2)) -> and(isUniversal(V1), isUniversal(V2)) isBool(_isNotEqualTo_(V1, V2)) -> and(isUniversal(V1), isUniversal(V2)) isBool(_or_(V1, V2)) -> and(isBool(V1), isBool(V2)) isBool(_xor_(V1, V2)) -> and(isBool(V1), isBool(V2))
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