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TRS Equational pair #487523227
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
n139.star.cs.uiowa.edu
space
Mixed_AC
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
19.6561369896 seconds
cpu usage
18.658658857
max memory
7.008256E7
stage attributes
key
value
output-size
129439
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR A B C U U' V1 V2 X) (THEORY (AC _and_ _or_ _xor_)) (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_(false,A) -> U31(isBool(A)) _and_(true,A) -> U41(isBool(A),A) _and_(A,_xor_(B,C)) -> U21(and(isBool(A),and(isBool(B),isBool(C))),A,B,C) _and_(A,A) -> U11(isBool(A),A) _implies_(A,B) -> U51(and(isBool(A),isBool(B)),A,B) _isEqualTo_(U,U) -> U71(isS(U)) _isEqualTo_(U,U') -> U61(and(isS(U'),isS(U)),U',U) _isNotEqualTo_(U,U) -> U91(isS(U)) _isNotEqualTo_(U,U') -> U81(and(isS(U'),isS(U)),U',U) _or_(A,B) -> U101(and(isBool(A),isBool(B)),A,B) _xor_(false,A) -> U121(isBool(A),A) _xor_(A,A) -> U111(isBool(A)) and(tt,X) -> X equal(X,X) -> tt if_then_else_fi(true,U,U') -> U141(and(isS(U'),isS(U)),U) if_then_else_fi(B,U,U') -> U131(and(isBool(B),and(isS(U'),isS(U))),B,U') 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)) isBool(not_(V1)) -> isBool(V1) isBool(false) -> tt isBool(true) -> tt not_(false) -> true not_(true) -> false not_(A) -> U151(isBool(A),A) ) Problem 1: Dependency Pairs Processor: -> FAxioms: _AND_(_and_(x8,x9),x10) = _AND_(x8,_and_(x9,x10)) _AND_(x8,x9) = _AND_(x9,x8) _OR_(_or_(x8,x9),x10) = _OR_(x8,_or_(x9,x10)) _OR_(x8,x9) = _OR_(x9,x8) _XOR_(_xor_(x8,x9),x10) = _XOR_(x8,_xor_(x9,x10)) _XOR_(x8,x9) = _XOR_(x9,x8) -> Pairs: U101#(tt,A,B) -> _AND_(A,B) U101#(tt,A,B) -> _XOR_(_and_(A,B),_xor_(A,B)) U101#(tt,A,B) -> _XOR_(A,B) U131#(tt,B,U') -> U132#(equal(_isNotEqualTo_(B,true),true),U') U131#(tt,B,U') -> _ISNOTEQUALTO_(B,true) U131#(tt,B,U') -> EQUAL(_isNotEqualTo_(B,true),true) U151#(tt,A) -> _XOR_(A,true) U21#(tt,A,B,C) -> _AND_(A,B) U21#(tt,A,B,C) -> _AND_(A,C) U21#(tt,A,B,C) -> _XOR_(_and_(A,B),_and_(A,C)) U51#(tt,A,B) -> _AND_(A,B) U51#(tt,A,B) -> _XOR_(A,_and_(A,B)) U51#(tt,A,B) -> NOT_(_xor_(A,_and_(A,B))) U61#(tt,U',U) -> U62#(equal(_isNotEqualTo_(U,U'),true)) U61#(tt,U',U) -> _ISNOTEQUALTO_(U,U') U61#(tt,U',U) -> EQUAL(_isNotEqualTo_(U,U'),true) U81#(tt,U',U) -> _ISEQUALTO_(U,U') U81#(tt,U',U) -> IF_THEN_ELSE_FI(_isEqualTo_(U,U'),false,true) _AND_(_and_(false,A),x8) -> U31#(isBool(A)) _AND_(_and_(false,A),x8) -> _AND_(U31(isBool(A)),x8) _AND_(_and_(false,A),x8) -> ISBOOL(A) _AND_(_and_(true,A),x8) -> U41#(isBool(A),A) _AND_(_and_(true,A),x8) -> _AND_(U41(isBool(A),A),x8) _AND_(_and_(true,A),x8) -> ISBOOL(A) _AND_(_and_(A,_xor_(B,C)),x8) -> U21#(and(isBool(A),and(isBool(B),isBool(C))),A,B,C) _AND_(_and_(A,_xor_(B,C)),x8) -> _AND_(U21(and(isBool(A),and(isBool(B),isBool(C))),A,B,C),x8) _AND_(_and_(A,_xor_(B,C)),x8) -> AND(isBool(A),and(isBool(B),isBool(C))) _AND_(_and_(A,_xor_(B,C)),x8) -> AND(isBool(B),isBool(C))
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