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TRS_Equational 2019-03-21 05.09 pair #429997310
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
n045.star.cs.uiowa.edu
space
Mixed_AC
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
19.6075 seconds
cpu usage
18.7598
user time
16.173
system time
2.5868
max virtual memory
749720.0
max residence set size
60912.0
stage attributes
key
value
starexec-result
YES
output
18.70/19.59 YES 18.70/19.59 18.70/19.59 Problem 1: 18.70/19.59 18.70/19.59 (VAR A B C U U' V1 V2 X) 18.70/19.59 (THEORY 18.70/19.59 (AC _and_ _or_ _xor_)) 18.70/19.59 (RULES 18.70/19.59 U101(tt,A,B) -> _xor_(_and_(A,B),_xor_(A,B)) 18.70/19.59 U11(tt,A) -> A 18.70/19.59 U111(tt) -> false 18.70/19.59 U121(tt,A) -> A 18.70/19.59 U131(tt,B,U') -> U132(equal(_isNotEqualTo_(B,true),true),U') 18.70/19.59 U132(tt,U') -> U' 18.70/19.59 U141(tt,U) -> U 18.70/19.59 U151(tt,A) -> _xor_(A,true) 18.70/19.59 U21(tt,A,B,C) -> _xor_(_and_(A,B),_and_(A,C)) 18.70/19.59 U31(tt) -> false 18.70/19.59 U41(tt,A) -> A 18.70/19.59 U51(tt,A,B) -> not_(_xor_(A,_and_(A,B))) 18.70/19.59 U61(tt,U',U) -> U62(equal(_isNotEqualTo_(U,U'),true)) 18.70/19.59 U62(tt) -> false 18.70/19.59 U71(tt) -> true 18.70/19.59 U81(tt,U',U) -> if_then_else_fi(_isEqualTo_(U,U'),false,true) 18.70/19.59 U91(tt) -> false 18.70/19.59 _and_(false,A) -> U31(isBool(A)) 18.70/19.59 _and_(true,A) -> U41(isBool(A),A) 18.70/19.59 _and_(A,_xor_(B,C)) -> U21(and(isBool(A),and(isBool(B),isBool(C))),A,B,C) 18.70/19.59 _and_(A,A) -> U11(isBool(A),A) 18.70/19.59 _implies_(A,B) -> U51(and(isBool(A),isBool(B)),A,B) 18.70/19.59 _isEqualTo_(U,U) -> U71(isS(U)) 18.70/19.59 _isEqualTo_(U,U') -> U61(and(isS(U'),isS(U)),U',U) 18.70/19.59 _isNotEqualTo_(U,U) -> U91(isS(U)) 18.70/19.59 _isNotEqualTo_(U,U') -> U81(and(isS(U'),isS(U)),U',U) 18.70/19.59 _or_(A,B) -> U101(and(isBool(A),isBool(B)),A,B) 18.70/19.59 _xor_(false,A) -> U121(isBool(A),A) 18.70/19.59 _xor_(A,A) -> U111(isBool(A)) 18.70/19.59 and(tt,X) -> X 18.70/19.59 equal(X,X) -> tt 18.70/19.59 if_then_else_fi(true,U,U') -> U141(and(isS(U'),isS(U)),U) 18.70/19.59 if_then_else_fi(B,U,U') -> U131(and(isBool(B),and(isS(U'),isS(U))),B,U') 18.70/19.59 isBool(_and_(V1,V2)) -> and(isBool(V1),isBool(V2)) 18.70/19.59 isBool(_implies_(V1,V2)) -> and(isBool(V1),isBool(V2)) 18.70/19.59 isBool(_isEqualTo_(V1,V2)) -> and(isUniversal(V1),isUniversal(V2)) 18.70/19.59 isBool(_isNotEqualTo_(V1,V2)) -> and(isUniversal(V1),isUniversal(V2)) 18.70/19.59 isBool(_or_(V1,V2)) -> and(isBool(V1),isBool(V2)) 18.70/19.59 isBool(_xor_(V1,V2)) -> and(isBool(V1),isBool(V2)) 18.70/19.59 isBool(not_(V1)) -> isBool(V1) 18.70/19.59 isBool(false) -> tt 18.70/19.59 isBool(true) -> tt 18.70/19.59 not_(false) -> true 18.70/19.59 not_(true) -> false 18.70/19.59 not_(A) -> U151(isBool(A),A) 18.70/19.59 ) 18.70/19.59 18.70/19.59 Problem 1: 18.70/19.59 18.70/19.59 Dependency Pairs Processor: 18.70/19.59 -> FAxioms: 18.70/19.59 _AND_(_and_(x8,x9),x10) = _AND_(x8,_and_(x9,x10)) 18.70/19.59 _AND_(x8,x9) = _AND_(x9,x8) 18.70/19.59 _OR_(_or_(x8,x9),x10) = _OR_(x8,_or_(x9,x10)) 18.70/19.59 _OR_(x8,x9) = _OR_(x9,x8) 18.70/19.59 _XOR_(_xor_(x8,x9),x10) = _XOR_(x8,_xor_(x9,x10)) 18.70/19.59 _XOR_(x8,x9) = _XOR_(x9,x8) 18.70/19.59 -> Pairs: 18.70/19.59 U101#(tt,A,B) -> _AND_(A,B) 18.70/19.59 U101#(tt,A,B) -> _XOR_(_and_(A,B),_xor_(A,B)) 18.70/19.59 U101#(tt,A,B) -> _XOR_(A,B) 18.70/19.59 U131#(tt,B,U') -> U132#(equal(_isNotEqualTo_(B,true),true),U') 18.70/19.59 U131#(tt,B,U') -> _ISNOTEQUALTO_(B,true) 18.70/19.59 U131#(tt,B,U') -> EQUAL(_isNotEqualTo_(B,true),true) 18.70/19.59 U151#(tt,A) -> _XOR_(A,true) 18.70/19.59 U21#(tt,A,B,C) -> _AND_(A,B) 18.70/19.59 U21#(tt,A,B,C) -> _AND_(A,C) 18.70/19.59 U21#(tt,A,B,C) -> _XOR_(_and_(A,B),_and_(A,C)) 18.70/19.59 U51#(tt,A,B) -> _AND_(A,B) 18.70/19.59 U51#(tt,A,B) -> _XOR_(A,_and_(A,B)) 18.70/19.59 U51#(tt,A,B) -> NOT_(_xor_(A,_and_(A,B))) 18.70/19.59 U61#(tt,U',U) -> U62#(equal(_isNotEqualTo_(U,U'),true)) 18.70/19.59 U61#(tt,U',U) -> _ISNOTEQUALTO_(U,U') 18.70/19.59 U61#(tt,U',U) -> EQUAL(_isNotEqualTo_(U,U'),true) 18.70/19.59 U81#(tt,U',U) -> _ISEQUALTO_(U,U') 18.70/19.59 U81#(tt,U',U) -> IF_THEN_ELSE_FI(_isEqualTo_(U,U'),false,true) 18.70/19.59 _AND_(_and_(false,A),x8) -> U31#(isBool(A)) 18.70/19.59 _AND_(_and_(false,A),x8) -> _AND_(U31(isBool(A)),x8) 18.70/19.59 _AND_(_and_(false,A),x8) -> ISBOOL(A) 18.70/19.59 _AND_(_and_(true,A),x8) -> U41#(isBool(A),A) 18.70/19.59 _AND_(_and_(true,A),x8) -> _AND_(U41(isBool(A),A),x8) 18.70/19.59 _AND_(_and_(true,A),x8) -> ISBOOL(A) 18.70/19.59 _AND_(_and_(A,_xor_(B,C)),x8) -> U21#(and(isBool(A),and(isBool(B),isBool(C))),A,B,C) 18.70/19.59 _AND_(_and_(A,_xor_(B,C)),x8) -> _AND_(U21(and(isBool(A),and(isBool(B),isBool(C))),A,B,C),x8) 18.70/19.59 _AND_(_and_(A,_xor_(B,C)),x8) -> AND(isBool(A),and(isBool(B),isBool(C))) 18.70/19.59 _AND_(_and_(A,_xor_(B,C)),x8) -> AND(isBool(B),isBool(C)) 18.70/19.59 _AND_(_and_(A,_xor_(B,C)),x8) -> ISBOOL(A) 18.70/19.59 _AND_(_and_(A,_xor_(B,C)),x8) -> ISBOOL(B) 18.70/19.59 _AND_(_and_(A,_xor_(B,C)),x8) -> ISBOOL(C) 18.70/19.59 _AND_(_and_(A,A),x8) -> U11#(isBool(A),A) 18.70/19.59 _AND_(_and_(A,A),x8) -> _AND_(U11(isBool(A),A),x8) 18.70/19.59 _AND_(_and_(A,A),x8) -> ISBOOL(A)
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