0.00/0.12 YES 0.00/0.12 0.00/0.12 Problem 1: 0.00/0.12 0.00/0.12 (VAR v_NonEmpty:S I:S P:S X:S X1:S X2:S Y:S Z:S) 0.00/0.12 (RULES 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ) 0.00/0.12 (STRATEGY INNERMOST) 0.00/0.12 0.00/0.12 Problem 1: 0.00/0.12 0.00/0.12 Dependency Pairs Processor: 0.00/0.12 -> Pairs: 0.00/0.12 U11#(mark(X:S)) -> U11#(X:S) 0.00/0.12 U11#(ok(X:S)) -> U11#(X:S) 0.00/0.12 U12#(mark(X:S)) -> U12#(X:S) 0.00/0.12 U12#(ok(X:S)) -> U12#(X:S) 0.00/0.12 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.12 __#(ok(X1:S),ok(X2:S)) -> __#(X1:S,X2:S) 0.00/0.12 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.12 ACTIVE(U11(X:S)) -> U11#(active(X:S)) 0.00/0.12 ACTIVE(U11(X:S)) -> ACTIVE(X:S) 0.00/0.12 ACTIVE(U12(X:S)) -> U12#(active(X:S)) 0.00/0.12 ACTIVE(U12(X:S)) -> ACTIVE(X:S) 0.00/0.12 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(X:S,__(Y:S,Z:S)) 0.00/0.12 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(Y:S,Z:S) 0.00/0.12 ACTIVE(__(X1:S,X2:S)) -> __#(active(X1:S),X2:S) 0.00/0.12 ACTIVE(__(X1:S,X2:S)) -> __#(X1:S,active(X2:S)) 0.00/0.12 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.12 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.12 ACTIVE(isNePal(X:S)) -> ACTIVE(X:S) 0.00/0.12 ACTIVE(isNePal(X:S)) -> ISNEPAL(active(X:S)) 0.00/0.12 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S) 0.00/0.12 ISNEPAL(ok(X:S)) -> ISNEPAL(X:S) 0.00/0.12 PROPER(U11(X:S)) -> U11#(proper(X:S)) 0.00/0.12 PROPER(U11(X:S)) -> PROPER(X:S) 0.00/0.12 PROPER(U12(X:S)) -> U12#(proper(X:S)) 0.00/0.12 PROPER(U12(X:S)) -> PROPER(X:S) 0.00/0.12 PROPER(__(X1:S,X2:S)) -> __#(proper(X1:S),proper(X2:S)) 0.00/0.12 PROPER(__(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.12 PROPER(__(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.12 PROPER(isNePal(X:S)) -> ISNEPAL(proper(X:S)) 0.00/0.12 PROPER(isNePal(X:S)) -> PROPER(X:S) 0.00/0.12 TOP(mark(X:S)) -> PROPER(X:S) 0.00/0.12 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.12 TOP(ok(X:S)) -> ACTIVE(X:S) 0.00/0.12 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 0.00/0.12 Problem 1: 0.00/0.12 0.00/0.12 SCC Processor: 0.00/0.12 -> Pairs: 0.00/0.12 U11#(mark(X:S)) -> U11#(X:S) 0.00/0.12 U11#(ok(X:S)) -> U11#(X:S) 0.00/0.12 U12#(mark(X:S)) -> U12#(X:S) 0.00/0.12 U12#(ok(X:S)) -> U12#(X:S) 0.00/0.12 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.12 __#(ok(X1:S),ok(X2:S)) -> __#(X1:S,X2:S) 0.00/0.12 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.12 ACTIVE(U11(X:S)) -> U11#(active(X:S)) 0.00/0.12 ACTIVE(U11(X:S)) -> ACTIVE(X:S) 0.00/0.12 ACTIVE(U12(X:S)) -> U12#(active(X:S)) 0.00/0.12 ACTIVE(U12(X:S)) -> ACTIVE(X:S) 0.00/0.12 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(X:S,__(Y:S,Z:S)) 0.00/0.12 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(Y:S,Z:S) 0.00/0.12 ACTIVE(__(X1:S,X2:S)) -> __#(active(X1:S),X2:S) 0.00/0.12 ACTIVE(__(X1:S,X2:S)) -> __#(X1:S,active(X2:S)) 0.00/0.12 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.12 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.12 ACTIVE(isNePal(X:S)) -> ACTIVE(X:S) 0.00/0.12 ACTIVE(isNePal(X:S)) -> ISNEPAL(active(X:S)) 0.00/0.12 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S) 0.00/0.12 ISNEPAL(ok(X:S)) -> ISNEPAL(X:S) 0.00/0.12 PROPER(U11(X:S)) -> U11#(proper(X:S)) 0.00/0.12 PROPER(U11(X:S)) -> PROPER(X:S) 0.00/0.12 PROPER(U12(X:S)) -> U12#(proper(X:S)) 0.00/0.12 PROPER(U12(X:S)) -> PROPER(X:S) 0.00/0.12 PROPER(__(X1:S,X2:S)) -> __#(proper(X1:S),proper(X2:S)) 0.00/0.12 PROPER(__(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.12 PROPER(__(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.12 PROPER(isNePal(X:S)) -> ISNEPAL(proper(X:S)) 0.00/0.12 PROPER(isNePal(X:S)) -> PROPER(X:S) 0.00/0.12 TOP(mark(X:S)) -> PROPER(X:S) 0.00/0.12 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.12 TOP(ok(X:S)) -> ACTIVE(X:S) 0.00/0.12 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->Strongly Connected Components: 0.00/0.12 ->->Cycle: 0.00/0.12 ->->-> Pairs: 0.00/0.12 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S) 0.00/0.12 ISNEPAL(ok(X:S)) -> ISNEPAL(X:S) 0.00/0.12 ->->-> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->->Cycle: 0.00/0.12 ->->-> Pairs: 0.00/0.12 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.12 __#(ok(X1:S),ok(X2:S)) -> __#(X1:S,X2:S) 0.00/0.12 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.12 ->->-> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->->Cycle: 0.00/0.12 ->->-> Pairs: 0.00/0.12 U12#(mark(X:S)) -> U12#(X:S) 0.00/0.12 U12#(ok(X:S)) -> U12#(X:S) 0.00/0.12 ->->-> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->->Cycle: 0.00/0.12 ->->-> Pairs: 0.00/0.12 U11#(mark(X:S)) -> U11#(X:S) 0.00/0.12 U11#(ok(X:S)) -> U11#(X:S) 0.00/0.12 ->->-> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->->Cycle: 0.00/0.12 ->->-> Pairs: 0.00/0.12 ACTIVE(U11(X:S)) -> ACTIVE(X:S) 0.00/0.12 ACTIVE(U12(X:S)) -> ACTIVE(X:S) 0.00/0.12 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.12 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.12 ACTIVE(isNePal(X:S)) -> ACTIVE(X:S) 0.00/0.12 ->->-> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->->Cycle: 0.00/0.12 ->->-> Pairs: 0.00/0.12 PROPER(U11(X:S)) -> PROPER(X:S) 0.00/0.12 PROPER(U12(X:S)) -> PROPER(X:S) 0.00/0.12 PROPER(__(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.12 PROPER(__(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.12 PROPER(isNePal(X:S)) -> PROPER(X:S) 0.00/0.12 ->->-> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->->Cycle: 0.00/0.12 ->->-> Pairs: 0.00/0.12 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.12 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.12 ->->-> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 0.00/0.12 0.00/0.12 The problem is decomposed in 7 subproblems. 0.00/0.12 0.00/0.12 Problem 1.1: 0.00/0.12 0.00/0.12 Subterm Processor: 0.00/0.12 -> Pairs: 0.00/0.12 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S) 0.00/0.12 ISNEPAL(ok(X:S)) -> ISNEPAL(X:S) 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->Projection: 0.00/0.12 pi(ISNEPAL) = 1 0.00/0.12 0.00/0.12 Problem 1.1: 0.00/0.12 0.00/0.12 SCC Processor: 0.00/0.12 -> Pairs: 0.00/0.12 Empty 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->Strongly Connected Components: 0.00/0.12 There is no strongly connected component 0.00/0.12 0.00/0.12 The problem is finite. 0.00/0.12 0.00/0.12 Problem 1.2: 0.00/0.12 0.00/0.12 Subterm Processor: 0.00/0.12 -> Pairs: 0.00/0.12 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.12 __#(ok(X1:S),ok(X2:S)) -> __#(X1:S,X2:S) 0.00/0.12 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->Projection: 0.00/0.12 pi(__#) = 1 0.00/0.12 0.00/0.12 Problem 1.2: 0.00/0.12 0.00/0.12 SCC Processor: 0.00/0.12 -> Pairs: 0.00/0.12 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->Strongly Connected Components: 0.00/0.12 ->->Cycle: 0.00/0.12 ->->-> Pairs: 0.00/0.12 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.12 ->->-> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 0.00/0.12 Problem 1.2: 0.00/0.12 0.00/0.12 Subterm Processor: 0.00/0.12 -> Pairs: 0.00/0.12 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->Projection: 0.00/0.12 pi(__#) = 2 0.00/0.12 0.00/0.12 Problem 1.2: 0.00/0.12 0.00/0.12 SCC Processor: 0.00/0.12 -> Pairs: 0.00/0.12 Empty 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->Strongly Connected Components: 0.00/0.12 There is no strongly connected component 0.00/0.12 0.00/0.12 The problem is finite. 0.00/0.12 0.00/0.12 Problem 1.3: 0.00/0.12 0.00/0.12 Subterm Processor: 0.00/0.12 -> Pairs: 0.00/0.12 U12#(mark(X:S)) -> U12#(X:S) 0.00/0.12 U12#(ok(X:S)) -> U12#(X:S) 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->Projection: 0.00/0.12 pi(U12#) = 1 0.00/0.12 0.00/0.12 Problem 1.3: 0.00/0.12 0.00/0.12 SCC Processor: 0.00/0.12 -> Pairs: 0.00/0.12 Empty 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->Strongly Connected Components: 0.00/0.12 There is no strongly connected component 0.00/0.12 0.00/0.12 The problem is finite. 0.00/0.12 0.00/0.12 Problem 1.4: 0.00/0.12 0.00/0.12 Subterm Processor: 0.00/0.12 -> Pairs: 0.00/0.12 U11#(mark(X:S)) -> U11#(X:S) 0.00/0.12 U11#(ok(X:S)) -> U11#(X:S) 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->Projection: 0.00/0.12 pi(U11#) = 1 0.00/0.12 0.00/0.12 Problem 1.4: 0.00/0.12 0.00/0.12 SCC Processor: 0.00/0.12 -> Pairs: 0.00/0.12 Empty 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->Strongly Connected Components: 0.00/0.12 There is no strongly connected component 0.00/0.12 0.00/0.12 The problem is finite. 0.00/0.12 0.00/0.12 Problem 1.5: 0.00/0.12 0.00/0.12 Subterm Processor: 0.00/0.12 -> Pairs: 0.00/0.12 ACTIVE(U11(X:S)) -> ACTIVE(X:S) 0.00/0.12 ACTIVE(U12(X:S)) -> ACTIVE(X:S) 0.00/0.12 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.12 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.12 ACTIVE(isNePal(X:S)) -> ACTIVE(X:S) 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->Projection: 0.00/0.12 pi(ACTIVE) = 1 0.00/0.12 0.00/0.12 Problem 1.5: 0.00/0.12 0.00/0.12 SCC Processor: 0.00/0.12 -> Pairs: 0.00/0.12 Empty 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->Strongly Connected Components: 0.00/0.12 There is no strongly connected component 0.00/0.12 0.00/0.12 The problem is finite. 0.00/0.12 0.00/0.12 Problem 1.6: 0.00/0.12 0.00/0.12 Subterm Processor: 0.00/0.12 -> Pairs: 0.00/0.12 PROPER(U11(X:S)) -> PROPER(X:S) 0.00/0.12 PROPER(U12(X:S)) -> PROPER(X:S) 0.00/0.12 PROPER(__(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.12 PROPER(__(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.12 PROPER(isNePal(X:S)) -> PROPER(X:S) 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->Projection: 0.00/0.12 pi(PROPER) = 1 0.00/0.12 0.00/0.12 Problem 1.6: 0.00/0.12 0.00/0.12 SCC Processor: 0.00/0.12 -> Pairs: 0.00/0.12 Empty 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->Strongly Connected Components: 0.00/0.12 There is no strongly connected component 0.00/0.12 0.00/0.12 The problem is finite. 0.00/0.12 0.00/0.12 Problem 1.7: 0.00/0.12 0.00/0.12 Reduction Pairs Processor: 0.00/0.12 -> Pairs: 0.00/0.12 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.12 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 -> Usable rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 ->Interpretation type: 0.00/0.12 Linear 0.00/0.12 ->Coefficients: 0.00/0.12 Natural Numbers 0.00/0.12 ->Dimension: 0.00/0.12 1 0.00/0.12 ->Bound: 0.00/0.12 2 0.00/0.12 ->Interpretation: 0.00/0.12 0.00/0.12 [U11](X) = 2.X + 2 0.00/0.12 [U12](X) = X + 2 0.00/0.12 [__](X1,X2) = 2.X1 + X2 + 2 0.00/0.12 [active](X) = X 0.00/0.12 [isNePal](X) = 2.X + 2 0.00/0.12 [proper](X) = X 0.00/0.12 [top](X) = 0 0.00/0.12 [fSNonEmpty] = 0 0.00/0.12 [mark](X) = X + 2 0.00/0.12 [nil] = 1 0.00/0.12 [ok](X) = X 0.00/0.12 [tt] = 2 0.00/0.12 [U11#](X) = 0 0.00/0.12 [U12#](X) = 0 0.00/0.12 [__#](X1,X2) = 0 0.00/0.12 [ACTIVE](X) = 0 0.00/0.12 [ISNEPAL](X) = 0 0.00/0.12 [PROPER](X) = 0 0.00/0.12 [TOP](X) = 2.X 0.00/0.12 0.00/0.12 Problem 1.7: 0.00/0.12 0.00/0.12 SCC Processor: 0.00/0.12 -> Pairs: 0.00/0.12 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->Strongly Connected Components: 0.00/0.12 ->->Cycle: 0.00/0.12 ->->-> Pairs: 0.00/0.12 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.12 ->->-> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 0.00/0.12 Problem 1.7: 0.00/0.12 0.00/0.12 Reduction Pairs Processor: 0.00/0.12 -> Pairs: 0.00/0.12 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 -> Usable rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 ->Interpretation type: 0.00/0.12 Linear 0.00/0.12 ->Coefficients: 0.00/0.12 Natural Numbers 0.00/0.12 ->Dimension: 0.00/0.12 1 0.00/0.12 ->Bound: 0.00/0.12 2 0.00/0.12 ->Interpretation: 0.00/0.12 0.00/0.12 [U11](X) = 2.X + 2 0.00/0.12 [U12](X) = 2.X + 2 0.00/0.12 [__](X1,X2) = X1 + X2 0.00/0.12 [active](X) = 2.X + 1 0.00/0.12 [isNePal](X) = 2.X + 2 0.00/0.12 [proper](X) = 0 0.00/0.12 [top](X) = 0 0.00/0.12 [fSNonEmpty] = 0 0.00/0.12 [mark](X) = X + 1 0.00/0.12 [nil] = 2 0.00/0.12 [ok](X) = 2.X + 2 0.00/0.12 [tt] = 1 0.00/0.12 [U11#](X) = 0 0.00/0.12 [U12#](X) = 0 0.00/0.12 [__#](X1,X2) = 0 0.00/0.12 [ACTIVE](X) = 0 0.00/0.12 [ISNEPAL](X) = 0 0.00/0.12 [PROPER](X) = 0 0.00/0.12 [TOP](X) = 2.X 0.00/0.12 0.00/0.12 Problem 1.7: 0.00/0.12 0.00/0.12 SCC Processor: 0.00/0.12 -> Pairs: 0.00/0.12 Empty 0.00/0.12 -> Rules: 0.00/0.12 U11(mark(X:S)) -> mark(U11(X:S)) 0.00/0.12 U11(ok(X:S)) -> ok(U11(X:S)) 0.00/0.12 U12(mark(X:S)) -> mark(U12(X:S)) 0.00/0.12 U12(ok(X:S)) -> ok(U12(X:S)) 0.00/0.12 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.12 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.12 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.12 active(U11(tt)) -> mark(U12(tt)) 0.00/0.12 active(U11(X:S)) -> U11(active(X:S)) 0.00/0.12 active(U12(tt)) -> mark(tt) 0.00/0.12 active(U12(X:S)) -> U12(active(X:S)) 0.00/0.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.12 active(__(nil,X:S)) -> mark(X:S) 0.00/0.12 active(__(X:S,nil)) -> mark(X:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.12 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt)) 0.00/0.12 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.12 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.12 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.12 proper(U11(X:S)) -> U11(proper(X:S)) 0.00/0.12 proper(U12(X:S)) -> U12(proper(X:S)) 0.00/0.12 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.12 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.12 proper(nil) -> ok(nil) 0.00/0.12 proper(tt) -> ok(tt) 0.00/0.12 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.12 top(ok(X:S)) -> top(active(X:S)) 0.00/0.12 ->Strongly Connected Components: 0.00/0.12 There is no strongly connected component 0.00/0.12 0.00/0.12 The problem is finite. 0.00/0.12 EOF