0.00/0.28 YES 0.00/0.28 0.00/0.28 Problem 1: 0.00/0.28 0.00/0.28 (VAR v_NonEmpty:S I:S P:S X:S X1:S X2:S Y:S Z:S) 0.00/0.28 (RULES 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 ) 0.00/0.28 (STRATEGY INNERMOST) 0.00/0.28 0.00/0.28 Problem 1: 0.00/0.28 0.00/0.28 Dependency Pairs Processor: 0.00/0.28 -> Pairs: 0.00/0.28 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.28 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.28 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S) 0.00/0.28 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.28 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(X:S,__(Y:S,Z:S)) 0.00/0.28 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(Y:S,Z:S) 0.00/0.28 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 0.00/0.28 ACTIVE(__(nil,X:S)) -> MARK(X:S) 0.00/0.28 ACTIVE(__(X:S,nil)) -> MARK(X:S) 0.00/0.28 ACTIVE(and(tt,X:S)) -> MARK(X:S) 0.00/0.28 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(tt) 0.00/0.28 AND(active(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.28 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.28 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S) 0.00/0.28 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S) 0.00/0.28 ISNEPAL(active(X:S)) -> ISNEPAL(X:S) 0.00/0.28 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S) 0.00/0.28 MARK(__(X1:S,X2:S)) -> __#(mark(X1:S),mark(X2:S)) 0.00/0.28 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 0.00/0.28 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.28 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.28 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.28 MARK(and(X1:S,X2:S)) -> AND(mark(X1:S),X2:S) 0.00/0.28 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.28 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S))) 0.00/0.28 MARK(isNePal(X:S)) -> ISNEPAL(mark(X:S)) 0.00/0.28 MARK(isNePal(X:S)) -> MARK(X:S) 0.00/0.28 -> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 0.00/0.28 Problem 1: 0.00/0.28 0.00/0.28 SCC Processor: 0.00/0.28 -> Pairs: 0.00/0.28 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.28 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.28 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S) 0.00/0.28 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.28 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(X:S,__(Y:S,Z:S)) 0.00/0.28 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(Y:S,Z:S) 0.00/0.28 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 0.00/0.28 ACTIVE(__(nil,X:S)) -> MARK(X:S) 0.00/0.28 ACTIVE(__(X:S,nil)) -> MARK(X:S) 0.00/0.28 ACTIVE(and(tt,X:S)) -> MARK(X:S) 0.00/0.28 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(tt) 0.00/0.28 AND(active(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.28 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.28 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S) 0.00/0.28 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S) 0.00/0.28 ISNEPAL(active(X:S)) -> ISNEPAL(X:S) 0.00/0.28 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S) 0.00/0.28 MARK(__(X1:S,X2:S)) -> __#(mark(X1:S),mark(X2:S)) 0.00/0.28 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 0.00/0.28 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.28 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.28 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.28 MARK(and(X1:S,X2:S)) -> AND(mark(X1:S),X2:S) 0.00/0.28 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.28 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S))) 0.00/0.28 MARK(isNePal(X:S)) -> ISNEPAL(mark(X:S)) 0.00/0.28 MARK(isNePal(X:S)) -> MARK(X:S) 0.00/0.28 -> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 ->Strongly Connected Components: 0.00/0.28 ->->Cycle: 0.00/0.28 ->->-> Pairs: 0.00/0.28 ISNEPAL(active(X:S)) -> ISNEPAL(X:S) 0.00/0.28 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S) 0.00/0.28 ->->-> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 ->->Cycle: 0.00/0.28 ->->-> Pairs: 0.00/0.28 AND(active(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.28 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.28 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S) 0.00/0.28 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S) 0.00/0.28 ->->-> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 ->->Cycle: 0.00/0.28 ->->-> Pairs: 0.00/0.28 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.28 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.28 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S) 0.00/0.28 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.28 ->->-> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 ->->Cycle: 0.00/0.28 ->->-> Pairs: 0.00/0.28 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 0.00/0.28 ACTIVE(__(nil,X:S)) -> MARK(X:S) 0.00/0.28 ACTIVE(__(X:S,nil)) -> MARK(X:S) 0.00/0.28 ACTIVE(and(tt,X:S)) -> MARK(X:S) 0.00/0.28 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 0.00/0.28 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.28 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.28 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.28 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.28 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S))) 0.00/0.28 MARK(isNePal(X:S)) -> MARK(X:S) 0.00/0.28 ->->-> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 0.00/0.28 0.00/0.28 The problem is decomposed in 4 subproblems. 0.00/0.28 0.00/0.28 Problem 1.1: 0.00/0.28 0.00/0.28 Subterm Processor: 0.00/0.28 -> Pairs: 0.00/0.28 ISNEPAL(active(X:S)) -> ISNEPAL(X:S) 0.00/0.28 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S) 0.00/0.28 -> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 ->Projection: 0.00/0.28 pi(ISNEPAL) = 1 0.00/0.28 0.00/0.28 Problem 1.1: 0.00/0.28 0.00/0.28 SCC Processor: 0.00/0.28 -> Pairs: 0.00/0.28 Empty 0.00/0.28 -> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 ->Strongly Connected Components: 0.00/0.28 There is no strongly connected component 0.00/0.28 0.00/0.28 The problem is finite. 0.00/0.28 0.00/0.28 Problem 1.2: 0.00/0.28 0.00/0.28 Subterm Processor: 0.00/0.28 -> Pairs: 0.00/0.28 AND(active(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.28 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.28 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S) 0.00/0.28 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S) 0.00/0.28 -> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 ->Projection: 0.00/0.28 pi(AND) = 1 0.00/0.28 0.00/0.28 Problem 1.2: 0.00/0.28 0.00/0.28 SCC Processor: 0.00/0.28 -> Pairs: 0.00/0.28 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S) 0.00/0.28 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S) 0.00/0.28 -> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 ->Strongly Connected Components: 0.00/0.28 ->->Cycle: 0.00/0.28 ->->-> Pairs: 0.00/0.28 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S) 0.00/0.28 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S) 0.00/0.28 ->->-> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 0.00/0.28 Problem 1.2: 0.00/0.28 0.00/0.28 Subterm Processor: 0.00/0.28 -> Pairs: 0.00/0.28 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S) 0.00/0.28 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S) 0.00/0.28 -> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 ->Projection: 0.00/0.28 pi(AND) = 2 0.00/0.28 0.00/0.28 Problem 1.2: 0.00/0.28 0.00/0.28 SCC Processor: 0.00/0.28 -> Pairs: 0.00/0.28 Empty 0.00/0.28 -> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 ->Strongly Connected Components: 0.00/0.28 There is no strongly connected component 0.00/0.28 0.00/0.28 The problem is finite. 0.00/0.28 0.00/0.28 Problem 1.3: 0.00/0.28 0.00/0.28 Subterm Processor: 0.00/0.28 -> Pairs: 0.00/0.28 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.28 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.28 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S) 0.00/0.28 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.28 -> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 ->Projection: 0.00/0.28 pi(__#) = 1 0.00/0.28 0.00/0.28 Problem 1.3: 0.00/0.28 0.00/0.28 SCC Processor: 0.00/0.28 -> Pairs: 0.00/0.28 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S) 0.00/0.28 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.28 -> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 ->Strongly Connected Components: 0.00/0.28 ->->Cycle: 0.00/0.28 ->->-> Pairs: 0.00/0.28 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S) 0.00/0.28 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.28 ->->-> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 0.00/0.28 Problem 1.3: 0.00/0.28 0.00/0.28 Subterm Processor: 0.00/0.28 -> Pairs: 0.00/0.28 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S) 0.00/0.28 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.28 -> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 ->Projection: 0.00/0.28 pi(__#) = 2 0.00/0.28 0.00/0.28 Problem 1.3: 0.00/0.28 0.00/0.28 SCC Processor: 0.00/0.28 -> Pairs: 0.00/0.28 Empty 0.00/0.28 -> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 ->Strongly Connected Components: 0.00/0.28 There is no strongly connected component 0.00/0.28 0.00/0.28 The problem is finite. 0.00/0.28 0.00/0.28 Problem 1.4: 0.00/0.28 0.00/0.28 Reduction Pairs Processor: 0.00/0.28 -> Pairs: 0.00/0.28 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 0.00/0.28 ACTIVE(__(nil,X:S)) -> MARK(X:S) 0.00/0.28 ACTIVE(__(X:S,nil)) -> MARK(X:S) 0.00/0.28 ACTIVE(and(tt,X:S)) -> MARK(X:S) 0.00/0.28 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 0.00/0.28 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.28 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.28 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.28 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.28 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S))) 0.00/0.28 MARK(isNePal(X:S)) -> MARK(X:S) 0.00/0.28 -> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 -> Usable rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.28 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.28 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.28 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.28 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.28 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.28 mark(nil) -> active(nil) 0.00/0.28 mark(tt) -> active(tt) 0.00/0.28 ->Interpretation type: 0.00/0.28 Linear 0.00/0.28 ->Coefficients: 0.00/0.28 Natural Numbers 0.00/0.28 ->Dimension: 0.00/0.28 1 0.00/0.28 ->Bound: 0.00/0.28 2 0.00/0.28 ->Interpretation: 0.00/0.28 0.00/0.28 [__](X1,X2) = 2.X1 + X2 + 2 0.00/0.28 [active](X) = X 0.00/0.28 [and](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.28 [isNePal](X) = 2.X + 1 0.00/0.28 [mark](X) = X 0.00/0.28 [fSNonEmpty] = 0 0.00/0.28 [nil] = 1 0.00/0.28 [tt] = 2 0.00/0.28 [__#](X1,X2) = 0 0.00/0.28 [ACTIVE](X) = 2.X + 2 0.00/0.28 [AND](X1,X2) = 0 0.00/0.28 [ISNEPAL](X) = 0 0.00/0.28 [MARK](X) = 2.X + 2 0.00/0.28 0.00/0.28 Problem 1.4: 0.00/0.28 0.00/0.28 SCC Processor: 0.00/0.28 -> Pairs: 0.00/0.28 ACTIVE(__(nil,X:S)) -> MARK(X:S) 0.00/0.28 ACTIVE(__(X:S,nil)) -> MARK(X:S) 0.00/0.28 ACTIVE(and(tt,X:S)) -> MARK(X:S) 0.00/0.28 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 0.00/0.28 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.28 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.28 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.28 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.28 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S))) 0.00/0.28 MARK(isNePal(X:S)) -> MARK(X:S) 0.00/0.28 -> Rules: 0.00/0.28 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.28 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.28 active(__(nil,X:S)) -> mark(X:S) 0.00/0.28 active(__(X:S,nil)) -> mark(X:S) 0.00/0.28 active(and(tt,X:S)) -> mark(X:S) 0.00/0.28 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.28 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.28 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.29 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.29 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.29 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.29 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.29 mark(nil) -> active(nil) 0.00/0.29 mark(tt) -> active(tt) 0.00/0.29 ->Strongly Connected Components: 0.00/0.29 ->->Cycle: 0.00/0.29 ->->-> Pairs: 0.00/0.29 ACTIVE(__(nil,X:S)) -> MARK(X:S) 0.00/0.29 ACTIVE(__(X:S,nil)) -> MARK(X:S) 0.00/0.29 ACTIVE(and(tt,X:S)) -> MARK(X:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.29 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S))) 0.00/0.29 MARK(isNePal(X:S)) -> MARK(X:S) 0.00/0.29 ->->-> Rules: 0.00/0.29 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.29 active(__(nil,X:S)) -> mark(X:S) 0.00/0.29 active(__(X:S,nil)) -> mark(X:S) 0.00/0.29 active(and(tt,X:S)) -> mark(X:S) 0.00/0.29 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.29 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.29 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.29 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.29 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.29 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.29 mark(nil) -> active(nil) 0.00/0.29 mark(tt) -> active(tt) 0.00/0.29 0.00/0.29 Problem 1.4: 0.00/0.29 0.00/0.29 Reduction Pairs Processor: 0.00/0.29 -> Pairs: 0.00/0.29 ACTIVE(__(nil,X:S)) -> MARK(X:S) 0.00/0.29 ACTIVE(__(X:S,nil)) -> MARK(X:S) 0.00/0.29 ACTIVE(and(tt,X:S)) -> MARK(X:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.29 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S))) 0.00/0.29 MARK(isNePal(X:S)) -> MARK(X:S) 0.00/0.29 -> Rules: 0.00/0.29 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.29 active(__(nil,X:S)) -> mark(X:S) 0.00/0.29 active(__(X:S,nil)) -> mark(X:S) 0.00/0.29 active(and(tt,X:S)) -> mark(X:S) 0.00/0.29 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.29 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.29 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.29 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.29 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.29 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.29 mark(nil) -> active(nil) 0.00/0.29 mark(tt) -> active(tt) 0.00/0.29 -> Usable rules: 0.00/0.29 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.29 active(__(nil,X:S)) -> mark(X:S) 0.00/0.29 active(__(X:S,nil)) -> mark(X:S) 0.00/0.29 active(and(tt,X:S)) -> mark(X:S) 0.00/0.29 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.29 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.29 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.29 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.29 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.29 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.29 mark(nil) -> active(nil) 0.00/0.29 mark(tt) -> active(tt) 0.00/0.29 ->Interpretation type: 0.00/0.29 Linear 0.00/0.29 ->Coefficients: 0.00/0.29 Natural Numbers 0.00/0.29 ->Dimension: 0.00/0.29 1 0.00/0.29 ->Bound: 0.00/0.29 2 0.00/0.29 ->Interpretation: 0.00/0.29 0.00/0.29 [__](X1,X2) = 2.X1 + X2 0.00/0.29 [active](X) = X 0.00/0.29 [and](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.29 [isNePal](X) = 2.X + 2 0.00/0.29 [mark](X) = X 0.00/0.29 [fSNonEmpty] = 0 0.00/0.29 [nil] = 2 0.00/0.29 [tt] = 0 0.00/0.29 [__#](X1,X2) = 0 0.00/0.29 [ACTIVE](X) = 2.X + 1 0.00/0.29 [AND](X1,X2) = 0 0.00/0.29 [ISNEPAL](X) = 0 0.00/0.29 [MARK](X) = 2.X + 2 0.00/0.29 0.00/0.29 Problem 1.4: 0.00/0.29 0.00/0.29 SCC Processor: 0.00/0.29 -> Pairs: 0.00/0.29 ACTIVE(__(X:S,nil)) -> MARK(X:S) 0.00/0.29 ACTIVE(and(tt,X:S)) -> MARK(X:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.29 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S))) 0.00/0.29 MARK(isNePal(X:S)) -> MARK(X:S) 0.00/0.29 -> Rules: 0.00/0.29 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.29 active(__(nil,X:S)) -> mark(X:S) 0.00/0.29 active(__(X:S,nil)) -> mark(X:S) 0.00/0.29 active(and(tt,X:S)) -> mark(X:S) 0.00/0.29 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.29 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.29 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.29 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.29 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.29 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.29 mark(nil) -> active(nil) 0.00/0.29 mark(tt) -> active(tt) 0.00/0.29 ->Strongly Connected Components: 0.00/0.29 ->->Cycle: 0.00/0.29 ->->-> Pairs: 0.00/0.29 ACTIVE(__(X:S,nil)) -> MARK(X:S) 0.00/0.29 ACTIVE(and(tt,X:S)) -> MARK(X:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.29 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S))) 0.00/0.29 MARK(isNePal(X:S)) -> MARK(X:S) 0.00/0.29 ->->-> Rules: 0.00/0.29 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.29 active(__(nil,X:S)) -> mark(X:S) 0.00/0.29 active(__(X:S,nil)) -> mark(X:S) 0.00/0.29 active(and(tt,X:S)) -> mark(X:S) 0.00/0.29 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.29 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.29 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.29 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.29 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.29 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.29 mark(nil) -> active(nil) 0.00/0.29 mark(tt) -> active(tt) 0.00/0.29 0.00/0.29 Problem 1.4: 0.00/0.29 0.00/0.29 Reduction Pairs Processor: 0.00/0.29 -> Pairs: 0.00/0.29 ACTIVE(__(X:S,nil)) -> MARK(X:S) 0.00/0.29 ACTIVE(and(tt,X:S)) -> MARK(X:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.29 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S))) 0.00/0.29 MARK(isNePal(X:S)) -> MARK(X:S) 0.00/0.29 -> Rules: 0.00/0.29 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.29 active(__(nil,X:S)) -> mark(X:S) 0.00/0.29 active(__(X:S,nil)) -> mark(X:S) 0.00/0.29 active(and(tt,X:S)) -> mark(X:S) 0.00/0.29 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.29 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.29 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.29 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.29 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.29 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.29 mark(nil) -> active(nil) 0.00/0.29 mark(tt) -> active(tt) 0.00/0.29 -> Usable rules: 0.00/0.29 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.29 active(__(nil,X:S)) -> mark(X:S) 0.00/0.29 active(__(X:S,nil)) -> mark(X:S) 0.00/0.29 active(and(tt,X:S)) -> mark(X:S) 0.00/0.29 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.29 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.29 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.29 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.29 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.29 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.29 mark(nil) -> active(nil) 0.00/0.29 mark(tt) -> active(tt) 0.00/0.29 ->Interpretation type: 0.00/0.29 Linear 0.00/0.29 ->Coefficients: 0.00/0.29 Natural Numbers 0.00/0.29 ->Dimension: 0.00/0.29 1 0.00/0.29 ->Bound: 0.00/0.29 2 0.00/0.29 ->Interpretation: 0.00/0.29 0.00/0.29 [__](X1,X2) = 2.X1 + X2 + 2 0.00/0.29 [active](X) = X 0.00/0.29 [and](X1,X2) = 2.X1 + 2.X2 0.00/0.29 [isNePal](X) = 2.X + 1 0.00/0.29 [mark](X) = X 0.00/0.29 [fSNonEmpty] = 0 0.00/0.29 [nil] = 2 0.00/0.29 [tt] = 2 0.00/0.29 [__#](X1,X2) = 0 0.00/0.29 [ACTIVE](X) = 2.X + 1 0.00/0.29 [AND](X1,X2) = 0 0.00/0.29 [ISNEPAL](X) = 0 0.00/0.29 [MARK](X) = 2.X + 1 0.00/0.29 0.00/0.29 Problem 1.4: 0.00/0.29 0.00/0.29 SCC Processor: 0.00/0.29 -> Pairs: 0.00/0.29 ACTIVE(and(tt,X:S)) -> MARK(X:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.29 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S))) 0.00/0.29 MARK(isNePal(X:S)) -> MARK(X:S) 0.00/0.29 -> Rules: 0.00/0.29 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.29 active(__(nil,X:S)) -> mark(X:S) 0.00/0.29 active(__(X:S,nil)) -> mark(X:S) 0.00/0.29 active(and(tt,X:S)) -> mark(X:S) 0.00/0.29 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.29 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.29 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.29 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.29 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.29 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.29 mark(nil) -> active(nil) 0.00/0.29 mark(tt) -> active(tt) 0.00/0.29 ->Strongly Connected Components: 0.00/0.29 ->->Cycle: 0.00/0.29 ->->-> Pairs: 0.00/0.29 ACTIVE(and(tt,X:S)) -> MARK(X:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.29 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S))) 0.00/0.29 MARK(isNePal(X:S)) -> MARK(X:S) 0.00/0.29 ->->-> Rules: 0.00/0.29 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.29 active(__(nil,X:S)) -> mark(X:S) 0.00/0.29 active(__(X:S,nil)) -> mark(X:S) 0.00/0.29 active(and(tt,X:S)) -> mark(X:S) 0.00/0.29 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.29 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.29 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.29 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.29 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.29 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.29 mark(nil) -> active(nil) 0.00/0.29 mark(tt) -> active(tt) 0.00/0.29 0.00/0.29 Problem 1.4: 0.00/0.29 0.00/0.29 Reduction Pairs Processor: 0.00/0.29 -> Pairs: 0.00/0.29 ACTIVE(and(tt,X:S)) -> MARK(X:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.29 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S))) 0.00/0.29 MARK(isNePal(X:S)) -> MARK(X:S) 0.00/0.29 -> Rules: 0.00/0.29 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.29 active(__(nil,X:S)) -> mark(X:S) 0.00/0.29 active(__(X:S,nil)) -> mark(X:S) 0.00/0.29 active(and(tt,X:S)) -> mark(X:S) 0.00/0.29 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.29 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.29 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.29 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.29 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.29 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.29 mark(nil) -> active(nil) 0.00/0.29 mark(tt) -> active(tt) 0.00/0.29 -> Usable rules: 0.00/0.29 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.29 active(__(nil,X:S)) -> mark(X:S) 0.00/0.29 active(__(X:S,nil)) -> mark(X:S) 0.00/0.29 active(and(tt,X:S)) -> mark(X:S) 0.00/0.29 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.29 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.29 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.29 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.29 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.29 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.29 mark(nil) -> active(nil) 0.00/0.29 mark(tt) -> active(tt) 0.00/0.29 ->Interpretation type: 0.00/0.29 Linear 0.00/0.29 ->Coefficients: 0.00/0.29 Natural Numbers 0.00/0.29 ->Dimension: 0.00/0.29 1 0.00/0.29 ->Bound: 0.00/0.29 2 0.00/0.29 ->Interpretation: 0.00/0.29 0.00/0.29 [__](X1,X2) = 2.X1 + X2 + 2 0.00/0.29 [active](X) = X 0.00/0.29 [and](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.29 [isNePal](X) = X + 2 0.00/0.29 [mark](X) = X 0.00/0.29 [fSNonEmpty] = 0 0.00/0.29 [nil] = 2 0.00/0.29 [tt] = 2 0.00/0.29 [__#](X1,X2) = 0 0.00/0.29 [ACTIVE](X) = X + 1 0.00/0.29 [AND](X1,X2) = 0 0.00/0.29 [ISNEPAL](X) = 0 0.00/0.29 [MARK](X) = 2.X 0.00/0.29 0.00/0.29 Problem 1.4: 0.00/0.29 0.00/0.29 SCC Processor: 0.00/0.29 -> Pairs: 0.00/0.29 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.29 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S))) 0.00/0.29 MARK(isNePal(X:S)) -> MARK(X:S) 0.00/0.29 -> Rules: 0.00/0.29 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.29 active(__(nil,X:S)) -> mark(X:S) 0.00/0.29 active(__(X:S,nil)) -> mark(X:S) 0.00/0.29 active(and(tt,X:S)) -> mark(X:S) 0.00/0.29 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.29 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.29 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.29 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.29 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.29 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.29 mark(nil) -> active(nil) 0.00/0.29 mark(tt) -> active(tt) 0.00/0.29 ->Strongly Connected Components: 0.00/0.29 ->->Cycle: 0.00/0.29 ->->-> Pairs: 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(isNePal(X:S)) -> MARK(X:S) 0.00/0.29 ->->-> Rules: 0.00/0.29 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.29 active(__(nil,X:S)) -> mark(X:S) 0.00/0.29 active(__(X:S,nil)) -> mark(X:S) 0.00/0.29 active(and(tt,X:S)) -> mark(X:S) 0.00/0.29 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.29 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.29 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.29 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.29 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.29 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.29 mark(nil) -> active(nil) 0.00/0.29 mark(tt) -> active(tt) 0.00/0.29 0.00/0.29 Problem 1.4: 0.00/0.29 0.00/0.29 Subterm Processor: 0.00/0.29 -> Pairs: 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(isNePal(X:S)) -> MARK(X:S) 0.00/0.29 -> Rules: 0.00/0.29 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.29 active(__(nil,X:S)) -> mark(X:S) 0.00/0.29 active(__(X:S,nil)) -> mark(X:S) 0.00/0.29 active(and(tt,X:S)) -> mark(X:S) 0.00/0.29 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.29 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.29 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.29 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.29 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.29 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.29 mark(nil) -> active(nil) 0.00/0.29 mark(tt) -> active(tt) 0.00/0.29 ->Projection: 0.00/0.29 pi(MARK) = 1 0.00/0.29 0.00/0.29 Problem 1.4: 0.00/0.29 0.00/0.29 SCC Processor: 0.00/0.29 -> Pairs: 0.00/0.29 Empty 0.00/0.29 -> Rules: 0.00/0.29 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 0.00/0.29 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.29 active(__(nil,X:S)) -> mark(X:S) 0.00/0.29 active(__(X:S,nil)) -> mark(X:S) 0.00/0.29 active(and(tt,X:S)) -> mark(X:S) 0.00/0.29 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.29 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.29 isNePal(active(X:S)) -> isNePal(X:S) 0.00/0.29 isNePal(mark(X:S)) -> isNePal(X:S) 0.00/0.29 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 0.00/0.29 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.29 mark(isNePal(X:S)) -> active(isNePal(mark(X:S))) 0.00/0.29 mark(nil) -> active(nil) 0.00/0.29 mark(tt) -> active(tt) 0.00/0.29 ->Strongly Connected Components: 0.00/0.29 There is no strongly connected component 0.00/0.29 0.00/0.29 The problem is finite. 0.00/0.29 EOF