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TRS Equational pair #487092792
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
n147.star.cs.uiowa.edu
space
Mixed_AC
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
19.3153 seconds
cpu usage
18.1173
user time
15.8065
system time
2.31079
max virtual memory
797752.0
max residence set size
43408.0
stage attributes
key
value
starexec-result
YES
output
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') U133#(tt,B,U') -> U134#(equal(_isNotEqualTo_(B,true),true),U') U133#(tt,B,U') -> _ISNOTEQUALTO_(B,true) U133#(tt,B,U') -> EQUAL(_isNotEqualTo_(B,true),true) U141#(tt,U) -> U142#(isS(U),U) U151#(tt,V2) -> U152#(isBool(V2)) U151#(tt,V2) -> ISBOOL(V2)
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