0.00/0.10 YES 0.00/0.10 0.00/0.10 Problem 1: 0.00/0.10 0.00/0.10 (VAR v_NonEmpty:S I:S P:S X:S X1:S X2:S Y:S Z:S) 0.00/0.10 (RULES 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ) 0.00/0.10 (STRATEGY INNERMOST) 0.00/0.10 0.00/0.10 Problem 1: 0.00/0.10 0.00/0.10 Dependency Pairs Processor: 0.00/0.10 -> Pairs: 0.00/0.10 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.10 __#(ok(X1:S),ok(X2:S)) -> __#(X1:S,X2:S) 0.00/0.10 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.10 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(X:S,__(Y:S,Z:S)) 0.00/0.10 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(Y:S,Z:S) 0.00/0.10 ACTIVE(__(X1:S,X2:S)) -> __#(active(X1:S),X2:S) 0.00/0.10 ACTIVE(__(X1:S,X2:S)) -> __#(X1:S,active(X2:S)) 0.00/0.10 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.10 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.10 ACTIVE(and(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.10 ACTIVE(and(X1:S,X2:S)) -> AND(active(X1:S),X2:S) 0.00/0.10 ACTIVE(isNePal(X:S)) -> ACTIVE(X:S) 0.00/0.10 ACTIVE(isNePal(X:S)) -> ISNEPAL(active(X:S)) 0.00/0.10 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.10 AND(ok(X1:S),ok(X2:S)) -> AND(X1:S,X2:S) 0.00/0.10 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S) 0.00/0.10 ISNEPAL(ok(X:S)) -> ISNEPAL(X:S) 0.00/0.10 PROPER(__(X1:S,X2:S)) -> __#(proper(X1:S),proper(X2:S)) 0.00/0.10 PROPER(__(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.10 PROPER(__(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.10 PROPER(and(X1:S,X2:S)) -> AND(proper(X1:S),proper(X2:S)) 0.00/0.10 PROPER(and(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.10 PROPER(and(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.10 PROPER(isNePal(X:S)) -> ISNEPAL(proper(X:S)) 0.00/0.10 PROPER(isNePal(X:S)) -> PROPER(X:S) 0.00/0.10 TOP(mark(X:S)) -> PROPER(X:S) 0.00/0.10 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.10 TOP(ok(X:S)) -> ACTIVE(X:S) 0.00/0.10 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.10 -> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 0.00/0.10 Problem 1: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.10 __#(ok(X1:S),ok(X2:S)) -> __#(X1:S,X2:S) 0.00/0.10 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.10 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(X:S,__(Y:S,Z:S)) 0.00/0.10 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(Y:S,Z:S) 0.00/0.10 ACTIVE(__(X1:S,X2:S)) -> __#(active(X1:S),X2:S) 0.00/0.10 ACTIVE(__(X1:S,X2:S)) -> __#(X1:S,active(X2:S)) 0.00/0.10 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.10 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.10 ACTIVE(and(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.10 ACTIVE(and(X1:S,X2:S)) -> AND(active(X1:S),X2:S) 0.00/0.10 ACTIVE(isNePal(X:S)) -> ACTIVE(X:S) 0.00/0.10 ACTIVE(isNePal(X:S)) -> ISNEPAL(active(X:S)) 0.00/0.10 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.10 AND(ok(X1:S),ok(X2:S)) -> AND(X1:S,X2:S) 0.00/0.10 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S) 0.00/0.10 ISNEPAL(ok(X:S)) -> ISNEPAL(X:S) 0.00/0.10 PROPER(__(X1:S,X2:S)) -> __#(proper(X1:S),proper(X2:S)) 0.00/0.10 PROPER(__(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.10 PROPER(__(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.10 PROPER(and(X1:S,X2:S)) -> AND(proper(X1:S),proper(X2:S)) 0.00/0.10 PROPER(and(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.10 PROPER(and(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.10 PROPER(isNePal(X:S)) -> ISNEPAL(proper(X:S)) 0.00/0.10 PROPER(isNePal(X:S)) -> PROPER(X:S) 0.00/0.10 TOP(mark(X:S)) -> PROPER(X:S) 0.00/0.10 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.10 TOP(ok(X:S)) -> ACTIVE(X:S) 0.00/0.10 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.10 -> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Strongly Connected Components: 0.00/0.10 ->->Cycle: 0.00/0.10 ->->-> Pairs: 0.00/0.10 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S) 0.00/0.10 ISNEPAL(ok(X:S)) -> ISNEPAL(X:S) 0.00/0.10 ->->-> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->->Cycle: 0.00/0.10 ->->-> Pairs: 0.00/0.10 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.10 AND(ok(X1:S),ok(X2:S)) -> AND(X1:S,X2:S) 0.00/0.10 ->->-> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->->Cycle: 0.00/0.10 ->->-> Pairs: 0.00/0.10 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.10 __#(ok(X1:S),ok(X2:S)) -> __#(X1:S,X2:S) 0.00/0.10 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.10 ->->-> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->->Cycle: 0.00/0.10 ->->-> Pairs: 0.00/0.10 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.10 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.10 ACTIVE(and(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.10 ACTIVE(isNePal(X:S)) -> ACTIVE(X:S) 0.00/0.10 ->->-> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->->Cycle: 0.00/0.10 ->->-> Pairs: 0.00/0.10 PROPER(__(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.10 PROPER(__(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.10 PROPER(and(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.10 PROPER(and(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.10 PROPER(isNePal(X:S)) -> PROPER(X:S) 0.00/0.10 ->->-> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->->Cycle: 0.00/0.10 ->->-> Pairs: 0.00/0.10 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.10 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.10 ->->-> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 0.00/0.10 0.00/0.10 The problem is decomposed in 6 subproblems. 0.00/0.10 0.00/0.10 Problem 1.1: 0.00/0.10 0.00/0.10 Subterm Processor: 0.00/0.10 -> Pairs: 0.00/0.10 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S) 0.00/0.10 ISNEPAL(ok(X:S)) -> ISNEPAL(X:S) 0.00/0.10 -> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Projection: 0.00/0.10 pi(ISNEPAL) = 1 0.00/0.10 0.00/0.10 Problem 1.1: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 Empty 0.00/0.10 -> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Strongly Connected Components: 0.00/0.10 There is no strongly connected component 0.00/0.10 0.00/0.10 The problem is finite. 0.00/0.10 0.00/0.10 Problem 1.2: 0.00/0.10 0.00/0.10 Subterm Processor: 0.00/0.10 -> Pairs: 0.00/0.10 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.10 AND(ok(X1:S),ok(X2:S)) -> AND(X1:S,X2:S) 0.00/0.10 -> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Projection: 0.00/0.10 pi(AND) = 1 0.00/0.10 0.00/0.10 Problem 1.2: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 Empty 0.00/0.10 -> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Strongly Connected Components: 0.00/0.10 There is no strongly connected component 0.00/0.10 0.00/0.10 The problem is finite. 0.00/0.10 0.00/0.10 Problem 1.3: 0.00/0.10 0.00/0.10 Subterm Processor: 0.00/0.10 -> Pairs: 0.00/0.10 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.10 __#(ok(X1:S),ok(X2:S)) -> __#(X1:S,X2:S) 0.00/0.10 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.10 -> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Projection: 0.00/0.10 pi(__#) = 1 0.00/0.10 0.00/0.10 Problem 1.3: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.10 -> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Strongly Connected Components: 0.00/0.10 ->->Cycle: 0.00/0.10 ->->-> Pairs: 0.00/0.10 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.10 ->->-> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 0.00/0.10 Problem 1.3: 0.00/0.10 0.00/0.10 Subterm Processor: 0.00/0.10 -> Pairs: 0.00/0.10 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.10 -> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Projection: 0.00/0.10 pi(__#) = 2 0.00/0.10 0.00/0.10 Problem 1.3: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 Empty 0.00/0.10 -> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Strongly Connected Components: 0.00/0.10 There is no strongly connected component 0.00/0.10 0.00/0.10 The problem is finite. 0.00/0.10 0.00/0.10 Problem 1.4: 0.00/0.10 0.00/0.10 Subterm Processor: 0.00/0.10 -> Pairs: 0.00/0.10 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.10 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.10 ACTIVE(and(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.10 ACTIVE(isNePal(X:S)) -> ACTIVE(X:S) 0.00/0.10 -> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Projection: 0.00/0.10 pi(ACTIVE) = 1 0.00/0.10 0.00/0.10 Problem 1.4: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 Empty 0.00/0.10 -> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Strongly Connected Components: 0.00/0.10 There is no strongly connected component 0.00/0.10 0.00/0.10 The problem is finite. 0.00/0.10 0.00/0.10 Problem 1.5: 0.00/0.10 0.00/0.10 Subterm Processor: 0.00/0.10 -> Pairs: 0.00/0.10 PROPER(__(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.10 PROPER(__(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.10 PROPER(and(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.10 PROPER(and(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.10 PROPER(isNePal(X:S)) -> PROPER(X:S) 0.00/0.10 -> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Projection: 0.00/0.10 pi(PROPER) = 1 0.00/0.10 0.00/0.10 Problem 1.5: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 Empty 0.00/0.10 -> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Strongly Connected Components: 0.00/0.10 There is no strongly connected component 0.00/0.10 0.00/0.10 The problem is finite. 0.00/0.10 0.00/0.10 Problem 1.6: 0.00/0.10 0.00/0.10 Reduction Pairs Processor: 0.00/0.10 -> Pairs: 0.00/0.10 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.10 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.10 -> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 -> Usable rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 ->Interpretation type: 0.00/0.10 Linear 0.00/0.10 ->Coefficients: 0.00/0.10 Natural Numbers 0.00/0.10 ->Dimension: 0.00/0.10 1 0.00/0.10 ->Bound: 0.00/0.10 2 0.00/0.10 ->Interpretation: 0.00/0.10 0.00/0.10 [__](X1,X2) = 2.X1 + X2 + 2 0.00/0.10 [active](X) = X 0.00/0.10 [and](X1,X2) = 2.X1 + X2 + 2 0.00/0.10 [isNePal](X) = X + 1 0.00/0.10 [proper](X) = X 0.00/0.10 [top](X) = 0 0.00/0.10 [fSNonEmpty] = 0 0.00/0.10 [mark](X) = X + 2 0.00/0.10 [nil] = 2 0.00/0.10 [ok](X) = X 0.00/0.10 [tt] = 0 0.00/0.10 [__#](X1,X2) = 0 0.00/0.10 [ACTIVE](X) = 0 0.00/0.10 [AND](X1,X2) = 0 0.00/0.10 [ISNEPAL](X) = 0 0.00/0.10 [PROPER](X) = 0 0.00/0.10 [TOP](X) = 2.X 0.00/0.10 0.00/0.10 Problem 1.6: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.10 -> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Strongly Connected Components: 0.00/0.10 ->->Cycle: 0.00/0.10 ->->-> Pairs: 0.00/0.10 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.10 ->->-> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 0.00/0.10 Problem 1.6: 0.00/0.10 0.00/0.10 Reduction Pairs Processor: 0.00/0.10 -> Pairs: 0.00/0.10 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.10 -> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 -> Usable rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 ->Interpretation type: 0.00/0.10 Linear 0.00/0.10 ->Coefficients: 0.00/0.10 Natural Numbers 0.00/0.10 ->Dimension: 0.00/0.10 1 0.00/0.10 ->Bound: 0.00/0.10 2 0.00/0.10 ->Interpretation: 0.00/0.10 0.00/0.10 [__](X1,X2) = 2.X2 + 2 0.00/0.10 [active](X) = 2.X + 1 0.00/0.10 [and](X1,X2) = X1 + X2 + 1 0.00/0.10 [isNePal](X) = 2.X + 2 0.00/0.10 [proper](X) = 0 0.00/0.10 [top](X) = 0 0.00/0.10 [fSNonEmpty] = 0 0.00/0.10 [mark](X) = 1 0.00/0.10 [nil] = 0 0.00/0.10 [ok](X) = 2.X + 2 0.00/0.10 [tt] = 2 0.00/0.10 [__#](X1,X2) = 0 0.00/0.10 [ACTIVE](X) = 0 0.00/0.10 [AND](X1,X2) = 0 0.00/0.10 [ISNEPAL](X) = 0 0.00/0.10 [PROPER](X) = 0 0.00/0.10 [TOP](X) = X 0.00/0.10 0.00/0.10 Problem 1.6: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 Empty 0.00/0.10 -> Rules: 0.00/0.10 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.10 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.10 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.10 active(__(nil,X:S)) -> mark(X:S) 0.00/0.10 active(__(X:S,nil)) -> mark(X:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.10 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.10 active(and(tt,X:S)) -> mark(X:S) 0.00/0.10 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(tt) 0.00/0.10 active(isNePal(X:S)) -> isNePal(active(X:S)) 0.00/0.10 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.10 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.10 isNePal(mark(X:S)) -> mark(isNePal(X:S)) 0.00/0.10 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.10 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.10 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.10 proper(nil) -> ok(nil) 0.00/0.10 proper(tt) -> ok(tt) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Strongly Connected Components: 0.00/0.10 There is no strongly connected component 0.00/0.10 0.00/0.10 The problem is finite. 0.00/0.10 EOF