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TRS Equational pair #487523230
details
property
value
status
complete
benchmark
RENAMED-BOOL_nokinds-noand.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
Mixed_AC
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
18.928591013 seconds
cpu usage
18.015303407
max memory
5.0061312E7
stage attributes
key
value
output-size
123766
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) -> U102(isBool(B),A,B) U102(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',U) -> U132(isS(U'),B,U',U) U132(tt,B,U',U) -> U133(isS(U),B,U') U133(tt,B,U') -> U134(equal(_isNotEqualTo_(B,true),true),U') U134(tt,U') -> U' U141(tt,U) -> U142(isS(U),U) U142(tt,U) -> U U151(tt,V2) -> U152(isBool(V2)) U152(tt) -> tt U161(tt,V2) -> U162(isBool(V2)) U162(tt) -> tt U171(tt,V2) -> U172(isUniversal(V2)) U172(tt) -> tt U181(tt,V2) -> U182(isUniversal(V2)) U182(tt) -> tt U191(tt,V2) -> U192(isBool(V2)) U192(tt) -> tt U201(tt,V2) -> U202(isBool(V2)) U202(tt) -> tt U21(tt,A,B,C) -> U22(isBool(B),A,B,C) U211(tt) -> tt U22(tt,A,B,C) -> U23(isBool(C),A,B,C) U221(tt,A) -> _xor_(A,true) U23(tt,A,B,C) -> _xor_(_and_(A,B),_and_(A,C)) U31(tt) -> false U41(tt,A) -> A U51(tt,A,B) -> U52(isBool(B),A,B) U52(tt,A,B) -> not_(_xor_(A,_and_(A,B))) U61(tt,U',U) -> U62(isS(U),U',U) U62(tt,U',U) -> U63(equal(_isNotEqualTo_(U,U'),true)) U63(tt) -> false U71(tt) -> true U81(tt,U',U) -> U82(isS(U),U',U) U82(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(isBool(A),A,B,C) _and_(A,A) -> U11(isBool(A),A) _implies_(A,B) -> U51(isBool(A),A,B) _isEqualTo_(U,U) -> U71(isS(U)) _isEqualTo_(U,U') -> U61(isS(U'),U',U) _isNotEqualTo_(U,U) -> U91(isS(U)) _isNotEqualTo_(U,U') -> U81(isS(U'),U',U) _or_(A,B) -> U101(isBool(A),A,B) _xor_(false,A) -> U121(isBool(A),A) _xor_(A,A) -> U111(isBool(A)) equal(X,X) -> tt if_then_else_fi(true,U,U') -> U141(isS(U'),U) if_then_else_fi(B,U,U') -> U131(isBool(B),B,U',U) isBool(_and_(V1,V2)) -> U151(isBool(V1),V2) isBool(_implies_(V1,V2)) -> U161(isBool(V1),V2) isBool(_isEqualTo_(V1,V2)) -> U171(isUniversal(V1),V2) isBool(_isNotEqualTo_(V1,V2)) -> U181(isUniversal(V1),V2) isBool(_or_(V1,V2)) -> U191(isBool(V1),V2) isBool(_xor_(V1,V2)) -> U201(isBool(V1),V2) isBool(not_(V1)) -> U211(isBool(V1)) isBool(false) -> tt isBool(true) -> tt not_(false) -> true not_(true) -> false not_(A) -> U221(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) -> U102#(isBool(B),A,B) U101#(tt,A,B) -> ISBOOL(B) U102#(tt,A,B) -> _AND_(A,B) U102#(tt,A,B) -> _XOR_(_and_(A,B),_xor_(A,B)) U102#(tt,A,B) -> _XOR_(A,B) U131#(tt,B,U',U) -> U132#(isS(U'),B,U',U) U132#(tt,B,U',U) -> U133#(isS(U),B,U')
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