0.00/0.20 YES 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 (VAR v_NonEmpty:S I:S P:S V:S V1:S V2:S X:S X1:S X2:S Y:S Z:S) 0.00/0.20 (RULES 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ) 0.00/0.20 (STRATEGY INNERMOST) 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 Dependency Pairs Processor: 0.00/0.20 -> Pairs: 0.00/0.20 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.20 __#(ok(X1:S),ok(X2:S)) -> __#(X1:S,X2:S) 0.00/0.20 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.20 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(X:S,__(Y:S,Z:S)) 0.00/0.20 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(Y:S,Z:S) 0.00/0.20 ACTIVE(__(X1:S,X2:S)) -> __#(active(X1:S),X2:S) 0.00/0.20 ACTIVE(__(X1:S,X2:S)) -> __#(X1:S,active(X2:S)) 0.00/0.20 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.20 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.20 ACTIVE(and(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.20 ACTIVE(and(X1:S,X2:S)) -> AND(active(X1:S),X2:S) 0.00/0.20 ACTIVE(isList(__(V1:S,V2:S))) -> AND(isList(V1:S),isList(V2:S)) 0.00/0.20 ACTIVE(isList(__(V1:S,V2:S))) -> ISLIST(V1:S) 0.00/0.20 ACTIVE(isList(__(V1:S,V2:S))) -> ISLIST(V2:S) 0.00/0.20 ACTIVE(isList(V:S)) -> ISNELIST(V:S) 0.00/0.20 ACTIVE(isNeList(__(V1:S,V2:S))) -> AND(isList(V1:S),isNeList(V2:S)) 0.00/0.20 ACTIVE(isNeList(__(V1:S,V2:S))) -> AND(isNeList(V1:S),isList(V2:S)) 0.00/0.20 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISLIST(V1:S) 0.00/0.20 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISLIST(V2:S) 0.00/0.20 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISNELIST(V1:S) 0.00/0.20 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISNELIST(V2:S) 0.00/0.20 ACTIVE(isNeList(V:S)) -> ISQID(V:S) 0.00/0.20 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> AND(isQid(I:S),isPal(P:S)) 0.00/0.20 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> ISPAL(P:S) 0.00/0.20 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> ISQID(I:S) 0.00/0.20 ACTIVE(isNePal(V:S)) -> ISQID(V:S) 0.00/0.20 ACTIVE(isPal(V:S)) -> ISNEPAL(V:S) 0.00/0.20 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.20 AND(ok(X1:S),ok(X2:S)) -> AND(X1:S,X2:S) 0.00/0.20 ISLIST(ok(X:S)) -> ISLIST(X:S) 0.00/0.20 ISNELIST(ok(X:S)) -> ISNELIST(X:S) 0.00/0.20 ISNEPAL(ok(X:S)) -> ISNEPAL(X:S) 0.00/0.20 ISPAL(ok(X:S)) -> ISPAL(X:S) 0.00/0.20 ISQID(ok(X:S)) -> ISQID(X:S) 0.00/0.20 PROPER(__(X1:S,X2:S)) -> __#(proper(X1:S),proper(X2:S)) 0.00/0.20 PROPER(__(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.20 PROPER(__(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.20 PROPER(and(X1:S,X2:S)) -> AND(proper(X1:S),proper(X2:S)) 0.00/0.20 PROPER(and(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.20 PROPER(and(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.20 PROPER(isList(X:S)) -> ISLIST(proper(X:S)) 0.00/0.20 PROPER(isList(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(isNeList(X:S)) -> ISNELIST(proper(X:S)) 0.00/0.20 PROPER(isNeList(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(isNePal(X:S)) -> ISNEPAL(proper(X:S)) 0.00/0.20 PROPER(isNePal(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(isPal(X:S)) -> ISPAL(proper(X:S)) 0.00/0.20 PROPER(isPal(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(isQid(X:S)) -> ISQID(proper(X:S)) 0.00/0.20 PROPER(isQid(X:S)) -> PROPER(X:S) 0.00/0.20 TOP(mark(X:S)) -> PROPER(X:S) 0.00/0.20 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.20 TOP(ok(X:S)) -> ACTIVE(X:S) 0.00/0.20 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.20 -> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.20 __#(ok(X1:S),ok(X2:S)) -> __#(X1:S,X2:S) 0.00/0.20 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.20 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(X:S,__(Y:S,Z:S)) 0.00/0.20 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(Y:S,Z:S) 0.00/0.20 ACTIVE(__(X1:S,X2:S)) -> __#(active(X1:S),X2:S) 0.00/0.20 ACTIVE(__(X1:S,X2:S)) -> __#(X1:S,active(X2:S)) 0.00/0.20 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.20 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.20 ACTIVE(and(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.20 ACTIVE(and(X1:S,X2:S)) -> AND(active(X1:S),X2:S) 0.00/0.20 ACTIVE(isList(__(V1:S,V2:S))) -> AND(isList(V1:S),isList(V2:S)) 0.00/0.20 ACTIVE(isList(__(V1:S,V2:S))) -> ISLIST(V1:S) 0.00/0.20 ACTIVE(isList(__(V1:S,V2:S))) -> ISLIST(V2:S) 0.00/0.20 ACTIVE(isList(V:S)) -> ISNELIST(V:S) 0.00/0.20 ACTIVE(isNeList(__(V1:S,V2:S))) -> AND(isList(V1:S),isNeList(V2:S)) 0.00/0.20 ACTIVE(isNeList(__(V1:S,V2:S))) -> AND(isNeList(V1:S),isList(V2:S)) 0.00/0.20 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISLIST(V1:S) 0.00/0.20 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISLIST(V2:S) 0.00/0.20 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISNELIST(V1:S) 0.00/0.20 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISNELIST(V2:S) 0.00/0.20 ACTIVE(isNeList(V:S)) -> ISQID(V:S) 0.00/0.20 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> AND(isQid(I:S),isPal(P:S)) 0.00/0.20 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> ISPAL(P:S) 0.00/0.20 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> ISQID(I:S) 0.00/0.20 ACTIVE(isNePal(V:S)) -> ISQID(V:S) 0.00/0.20 ACTIVE(isPal(V:S)) -> ISNEPAL(V:S) 0.00/0.20 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.20 AND(ok(X1:S),ok(X2:S)) -> AND(X1:S,X2:S) 0.00/0.20 ISLIST(ok(X:S)) -> ISLIST(X:S) 0.00/0.20 ISNELIST(ok(X:S)) -> ISNELIST(X:S) 0.00/0.20 ISNEPAL(ok(X:S)) -> ISNEPAL(X:S) 0.00/0.20 ISPAL(ok(X:S)) -> ISPAL(X:S) 0.00/0.20 ISQID(ok(X:S)) -> ISQID(X:S) 0.00/0.20 PROPER(__(X1:S,X2:S)) -> __#(proper(X1:S),proper(X2:S)) 0.00/0.20 PROPER(__(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.20 PROPER(__(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.20 PROPER(and(X1:S,X2:S)) -> AND(proper(X1:S),proper(X2:S)) 0.00/0.20 PROPER(and(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.20 PROPER(and(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.20 PROPER(isList(X:S)) -> ISLIST(proper(X:S)) 0.00/0.20 PROPER(isList(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(isNeList(X:S)) -> ISNELIST(proper(X:S)) 0.00/0.20 PROPER(isNeList(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(isNePal(X:S)) -> ISNEPAL(proper(X:S)) 0.00/0.20 PROPER(isNePal(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(isPal(X:S)) -> ISPAL(proper(X:S)) 0.00/0.20 PROPER(isPal(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(isQid(X:S)) -> ISQID(proper(X:S)) 0.00/0.20 PROPER(isQid(X:S)) -> PROPER(X:S) 0.00/0.20 TOP(mark(X:S)) -> PROPER(X:S) 0.00/0.20 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.20 TOP(ok(X:S)) -> ACTIVE(X:S) 0.00/0.20 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.20 -> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->Strongly Connected Components: 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 ISQID(ok(X:S)) -> ISQID(X:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 ISPAL(ok(X:S)) -> ISPAL(X:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 ISNEPAL(ok(X:S)) -> ISNEPAL(X:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 ISNELIST(ok(X:S)) -> ISNELIST(X:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 ISLIST(ok(X:S)) -> ISLIST(X:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.20 AND(ok(X1:S),ok(X2:S)) -> AND(X1:S,X2:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.20 __#(ok(X1:S),ok(X2:S)) -> __#(X1:S,X2:S) 0.00/0.20 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.20 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.20 ACTIVE(and(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 PROPER(__(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.20 PROPER(__(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.20 PROPER(and(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.20 PROPER(and(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.20 PROPER(isList(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(isNeList(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(isNePal(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(isPal(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(isQid(X:S)) -> PROPER(X:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.20 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.20 ->->-> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 0.00/0.20 0.00/0.20 The problem is decomposed in 10 subproblems. 0.00/0.20 0.00/0.20 Problem 1.1: 0.00/0.20 0.00/0.20 Subterm Processor: 0.00/0.20 -> Pairs: 0.00/0.20 ISQID(ok(X:S)) -> ISQID(X:S) 0.00/0.20 -> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->Projection: 0.00/0.20 pi(ISQID) = 1 0.00/0.20 0.00/0.20 Problem 1.1: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 Empty 0.00/0.20 -> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->Strongly Connected Components: 0.00/0.20 There is no strongly connected component 0.00/0.20 0.00/0.20 The problem is finite. 0.00/0.20 0.00/0.20 Problem 1.2: 0.00/0.20 0.00/0.20 Subterm Processor: 0.00/0.20 -> Pairs: 0.00/0.20 ISPAL(ok(X:S)) -> ISPAL(X:S) 0.00/0.20 -> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->Projection: 0.00/0.20 pi(ISPAL) = 1 0.00/0.20 0.00/0.20 Problem 1.2: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 Empty 0.00/0.20 -> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->Strongly Connected Components: 0.00/0.20 There is no strongly connected component 0.00/0.20 0.00/0.20 The problem is finite. 0.00/0.20 0.00/0.20 Problem 1.3: 0.00/0.20 0.00/0.20 Subterm Processor: 0.00/0.20 -> Pairs: 0.00/0.20 ISNEPAL(ok(X:S)) -> ISNEPAL(X:S) 0.00/0.20 -> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->Projection: 0.00/0.20 pi(ISNEPAL) = 1 0.00/0.20 0.00/0.20 Problem 1.3: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 Empty 0.00/0.20 -> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->Strongly Connected Components: 0.00/0.20 There is no strongly connected component 0.00/0.20 0.00/0.20 The problem is finite. 0.00/0.20 0.00/0.20 Problem 1.4: 0.00/0.20 0.00/0.20 Subterm Processor: 0.00/0.20 -> Pairs: 0.00/0.20 ISNELIST(ok(X:S)) -> ISNELIST(X:S) 0.00/0.20 -> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->Projection: 0.00/0.20 pi(ISNELIST) = 1 0.00/0.20 0.00/0.20 Problem 1.4: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 Empty 0.00/0.20 -> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->Strongly Connected Components: 0.00/0.20 There is no strongly connected component 0.00/0.20 0.00/0.20 The problem is finite. 0.00/0.20 0.00/0.20 Problem 1.5: 0.00/0.20 0.00/0.20 Subterm Processor: 0.00/0.20 -> Pairs: 0.00/0.20 ISLIST(ok(X:S)) -> ISLIST(X:S) 0.00/0.20 -> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 ->Projection: 0.00/0.20 pi(ISLIST) = 1 0.00/0.20 0.00/0.20 Problem 1.5: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 Empty 0.00/0.20 -> Rules: 0.00/0.20 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.20 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.20 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.20 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.20 active(__(nil,X:S)) -> mark(X:S) 0.00/0.20 active(__(X:S,nil)) -> mark(X:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.20 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.20 active(and(tt,X:S)) -> mark(X:S) 0.00/0.20 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.20 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.20 active(isList(nil)) -> mark(tt) 0.00/0.20 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.20 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.20 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.20 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.20 active(isPal(nil)) -> mark(tt) 0.00/0.20 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.20 active(isQid(a)) -> mark(tt) 0.00/0.20 active(isQid(e)) -> mark(tt) 0.00/0.20 active(isQid(i)) -> mark(tt) 0.00/0.20 active(isQid(o)) -> mark(tt) 0.00/0.20 active(isQid(u)) -> mark(tt) 0.00/0.20 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.20 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.20 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.20 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.20 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.20 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.20 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.20 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.20 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.20 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.20 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.20 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.20 proper(a) -> ok(a) 0.00/0.20 proper(e) -> ok(e) 0.00/0.20 proper(i) -> ok(i) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 proper(o) -> ok(o) 0.00/0.20 proper(tt) -> ok(tt) 0.00/0.20 proper(u) -> ok(u) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 There is no strongly connected component 0.00/0.21 0.00/0.21 The problem is finite. 0.00/0.21 0.00/0.21 Problem 1.6: 0.00/0.21 0.00/0.21 Subterm Processor: 0.00/0.21 -> Pairs: 0.00/0.21 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.21 AND(ok(X1:S),ok(X2:S)) -> AND(X1:S,X2:S) 0.00/0.21 -> Rules: 0.00/0.21 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.21 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.21 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.21 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.21 active(__(nil,X:S)) -> mark(X:S) 0.00/0.21 active(__(X:S,nil)) -> mark(X:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.21 active(and(tt,X:S)) -> mark(X:S) 0.00/0.21 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.21 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.21 active(isList(nil)) -> mark(tt) 0.00/0.21 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.21 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.21 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isPal(nil)) -> mark(tt) 0.00/0.21 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.21 active(isQid(a)) -> mark(tt) 0.00/0.21 active(isQid(e)) -> mark(tt) 0.00/0.21 active(isQid(i)) -> mark(tt) 0.00/0.21 active(isQid(o)) -> mark(tt) 0.00/0.21 active(isQid(u)) -> mark(tt) 0.00/0.21 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.21 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.21 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.21 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.21 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.21 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.21 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.21 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.21 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.21 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.21 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.21 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.21 proper(a) -> ok(a) 0.00/0.21 proper(e) -> ok(e) 0.00/0.21 proper(i) -> ok(i) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 proper(o) -> ok(o) 0.00/0.21 proper(tt) -> ok(tt) 0.00/0.21 proper(u) -> ok(u) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 ->Projection: 0.00/0.21 pi(AND) = 1 0.00/0.21 0.00/0.21 Problem 1.6: 0.00/0.21 0.00/0.21 SCC Processor: 0.00/0.21 -> Pairs: 0.00/0.21 Empty 0.00/0.21 -> Rules: 0.00/0.21 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.21 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.21 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.21 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.21 active(__(nil,X:S)) -> mark(X:S) 0.00/0.21 active(__(X:S,nil)) -> mark(X:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.21 active(and(tt,X:S)) -> mark(X:S) 0.00/0.21 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.21 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.21 active(isList(nil)) -> mark(tt) 0.00/0.21 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.21 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.21 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isPal(nil)) -> mark(tt) 0.00/0.21 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.21 active(isQid(a)) -> mark(tt) 0.00/0.21 active(isQid(e)) -> mark(tt) 0.00/0.21 active(isQid(i)) -> mark(tt) 0.00/0.21 active(isQid(o)) -> mark(tt) 0.00/0.21 active(isQid(u)) -> mark(tt) 0.00/0.21 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.21 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.21 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.21 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.21 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.21 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.21 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.21 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.21 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.21 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.21 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.21 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.21 proper(a) -> ok(a) 0.00/0.21 proper(e) -> ok(e) 0.00/0.21 proper(i) -> ok(i) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 proper(o) -> ok(o) 0.00/0.21 proper(tt) -> ok(tt) 0.00/0.21 proper(u) -> ok(u) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 There is no strongly connected component 0.00/0.21 0.00/0.21 The problem is finite. 0.00/0.21 0.00/0.21 Problem 1.7: 0.00/0.21 0.00/0.21 Subterm Processor: 0.00/0.21 -> Pairs: 0.00/0.21 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 0.00/0.21 __#(ok(X1:S),ok(X2:S)) -> __#(X1:S,X2:S) 0.00/0.21 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.21 -> Rules: 0.00/0.21 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.21 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.21 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.21 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.21 active(__(nil,X:S)) -> mark(X:S) 0.00/0.21 active(__(X:S,nil)) -> mark(X:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.21 active(and(tt,X:S)) -> mark(X:S) 0.00/0.21 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.21 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.21 active(isList(nil)) -> mark(tt) 0.00/0.21 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.21 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.21 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isPal(nil)) -> mark(tt) 0.00/0.21 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.21 active(isQid(a)) -> mark(tt) 0.00/0.21 active(isQid(e)) -> mark(tt) 0.00/0.21 active(isQid(i)) -> mark(tt) 0.00/0.21 active(isQid(o)) -> mark(tt) 0.00/0.21 active(isQid(u)) -> mark(tt) 0.00/0.21 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.21 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.21 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.21 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.21 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.21 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.21 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.21 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.21 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.21 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.21 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.21 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.21 proper(a) -> ok(a) 0.00/0.21 proper(e) -> ok(e) 0.00/0.21 proper(i) -> ok(i) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 proper(o) -> ok(o) 0.00/0.21 proper(tt) -> ok(tt) 0.00/0.21 proper(u) -> ok(u) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 ->Projection: 0.00/0.21 pi(__#) = 1 0.00/0.21 0.00/0.21 Problem 1.7: 0.00/0.21 0.00/0.21 SCC Processor: 0.00/0.21 -> Pairs: 0.00/0.21 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.21 -> Rules: 0.00/0.21 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.21 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.21 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.21 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.21 active(__(nil,X:S)) -> mark(X:S) 0.00/0.21 active(__(X:S,nil)) -> mark(X:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.21 active(and(tt,X:S)) -> mark(X:S) 0.00/0.21 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.21 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.21 active(isList(nil)) -> mark(tt) 0.00/0.21 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.21 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.21 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isPal(nil)) -> mark(tt) 0.00/0.21 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.21 active(isQid(a)) -> mark(tt) 0.00/0.21 active(isQid(e)) -> mark(tt) 0.00/0.21 active(isQid(i)) -> mark(tt) 0.00/0.21 active(isQid(o)) -> mark(tt) 0.00/0.21 active(isQid(u)) -> mark(tt) 0.00/0.21 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.21 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.21 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.21 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.21 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.21 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.21 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.21 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.21 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.21 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.21 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.21 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.21 proper(a) -> ok(a) 0.00/0.21 proper(e) -> ok(e) 0.00/0.21 proper(i) -> ok(i) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 proper(o) -> ok(o) 0.00/0.21 proper(tt) -> ok(tt) 0.00/0.21 proper(u) -> ok(u) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 ->->Cycle: 0.00/0.21 ->->-> Pairs: 0.00/0.21 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.21 ->->-> Rules: 0.00/0.21 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.21 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.21 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.21 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.21 active(__(nil,X:S)) -> mark(X:S) 0.00/0.21 active(__(X:S,nil)) -> mark(X:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.21 active(and(tt,X:S)) -> mark(X:S) 0.00/0.21 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.21 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.21 active(isList(nil)) -> mark(tt) 0.00/0.21 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.21 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.21 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isPal(nil)) -> mark(tt) 0.00/0.21 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.21 active(isQid(a)) -> mark(tt) 0.00/0.21 active(isQid(e)) -> mark(tt) 0.00/0.21 active(isQid(i)) -> mark(tt) 0.00/0.21 active(isQid(o)) -> mark(tt) 0.00/0.21 active(isQid(u)) -> mark(tt) 0.00/0.21 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.21 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.21 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.21 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.21 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.21 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.21 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.21 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.21 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.21 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.21 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.21 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.21 proper(a) -> ok(a) 0.00/0.21 proper(e) -> ok(e) 0.00/0.21 proper(i) -> ok(i) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 proper(o) -> ok(o) 0.00/0.21 proper(tt) -> ok(tt) 0.00/0.21 proper(u) -> ok(u) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 0.00/0.21 Problem 1.7: 0.00/0.21 0.00/0.21 Subterm Processor: 0.00/0.21 -> Pairs: 0.00/0.21 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 0.00/0.21 -> Rules: 0.00/0.21 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.21 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.21 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.21 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.21 active(__(nil,X:S)) -> mark(X:S) 0.00/0.21 active(__(X:S,nil)) -> mark(X:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.21 active(and(tt,X:S)) -> mark(X:S) 0.00/0.21 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.21 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.21 active(isList(nil)) -> mark(tt) 0.00/0.21 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.21 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.21 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isPal(nil)) -> mark(tt) 0.00/0.21 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.21 active(isQid(a)) -> mark(tt) 0.00/0.21 active(isQid(e)) -> mark(tt) 0.00/0.21 active(isQid(i)) -> mark(tt) 0.00/0.21 active(isQid(o)) -> mark(tt) 0.00/0.21 active(isQid(u)) -> mark(tt) 0.00/0.21 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.21 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.21 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.21 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.21 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.21 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.21 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.21 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.21 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.21 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.21 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.21 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.21 proper(a) -> ok(a) 0.00/0.21 proper(e) -> ok(e) 0.00/0.21 proper(i) -> ok(i) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 proper(o) -> ok(o) 0.00/0.21 proper(tt) -> ok(tt) 0.00/0.21 proper(u) -> ok(u) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 ->Projection: 0.00/0.21 pi(__#) = 2 0.00/0.21 0.00/0.21 Problem 1.7: 0.00/0.21 0.00/0.21 SCC Processor: 0.00/0.21 -> Pairs: 0.00/0.21 Empty 0.00/0.21 -> Rules: 0.00/0.21 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.21 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.21 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.21 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.21 active(__(nil,X:S)) -> mark(X:S) 0.00/0.21 active(__(X:S,nil)) -> mark(X:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.21 active(and(tt,X:S)) -> mark(X:S) 0.00/0.21 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.21 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.21 active(isList(nil)) -> mark(tt) 0.00/0.21 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.21 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.21 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isPal(nil)) -> mark(tt) 0.00/0.21 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.21 active(isQid(a)) -> mark(tt) 0.00/0.21 active(isQid(e)) -> mark(tt) 0.00/0.21 active(isQid(i)) -> mark(tt) 0.00/0.21 active(isQid(o)) -> mark(tt) 0.00/0.21 active(isQid(u)) -> mark(tt) 0.00/0.21 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.21 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.21 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.21 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.21 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.21 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.21 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.21 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.21 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.21 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.21 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.21 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.21 proper(a) -> ok(a) 0.00/0.21 proper(e) -> ok(e) 0.00/0.21 proper(i) -> ok(i) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 proper(o) -> ok(o) 0.00/0.21 proper(tt) -> ok(tt) 0.00/0.21 proper(u) -> ok(u) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 There is no strongly connected component 0.00/0.21 0.00/0.21 The problem is finite. 0.00/0.21 0.00/0.21 Problem 1.8: 0.00/0.21 0.00/0.21 Subterm Processor: 0.00/0.21 -> Pairs: 0.00/0.21 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.21 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.21 ACTIVE(and(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.21 -> Rules: 0.00/0.21 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.21 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.21 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.21 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.21 active(__(nil,X:S)) -> mark(X:S) 0.00/0.21 active(__(X:S,nil)) -> mark(X:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.21 active(and(tt,X:S)) -> mark(X:S) 0.00/0.21 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.21 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.21 active(isList(nil)) -> mark(tt) 0.00/0.21 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.21 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.21 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isPal(nil)) -> mark(tt) 0.00/0.21 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.21 active(isQid(a)) -> mark(tt) 0.00/0.21 active(isQid(e)) -> mark(tt) 0.00/0.21 active(isQid(i)) -> mark(tt) 0.00/0.21 active(isQid(o)) -> mark(tt) 0.00/0.21 active(isQid(u)) -> mark(tt) 0.00/0.21 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.21 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.21 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.21 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.21 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.21 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.21 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.21 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.21 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.21 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.21 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.21 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.21 proper(a) -> ok(a) 0.00/0.21 proper(e) -> ok(e) 0.00/0.21 proper(i) -> ok(i) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 proper(o) -> ok(o) 0.00/0.21 proper(tt) -> ok(tt) 0.00/0.21 proper(u) -> ok(u) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 ->Projection: 0.00/0.21 pi(ACTIVE) = 1 0.00/0.21 0.00/0.21 Problem 1.8: 0.00/0.21 0.00/0.21 SCC Processor: 0.00/0.21 -> Pairs: 0.00/0.21 Empty 0.00/0.21 -> Rules: 0.00/0.21 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.21 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.21 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.21 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.21 active(__(nil,X:S)) -> mark(X:S) 0.00/0.21 active(__(X:S,nil)) -> mark(X:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.21 active(and(tt,X:S)) -> mark(X:S) 0.00/0.21 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.21 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.21 active(isList(nil)) -> mark(tt) 0.00/0.21 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.21 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.21 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isPal(nil)) -> mark(tt) 0.00/0.21 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.21 active(isQid(a)) -> mark(tt) 0.00/0.21 active(isQid(e)) -> mark(tt) 0.00/0.21 active(isQid(i)) -> mark(tt) 0.00/0.21 active(isQid(o)) -> mark(tt) 0.00/0.21 active(isQid(u)) -> mark(tt) 0.00/0.21 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.21 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.21 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.21 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.21 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.21 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.21 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.21 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.21 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.21 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.21 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.21 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.21 proper(a) -> ok(a) 0.00/0.21 proper(e) -> ok(e) 0.00/0.21 proper(i) -> ok(i) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 proper(o) -> ok(o) 0.00/0.21 proper(tt) -> ok(tt) 0.00/0.21 proper(u) -> ok(u) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 There is no strongly connected component 0.00/0.21 0.00/0.21 The problem is finite. 0.00/0.21 0.00/0.21 Problem 1.9: 0.00/0.21 0.00/0.21 Subterm Processor: 0.00/0.21 -> Pairs: 0.00/0.21 PROPER(__(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.21 PROPER(__(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.21 PROPER(and(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.21 PROPER(and(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.21 PROPER(isList(X:S)) -> PROPER(X:S) 0.00/0.21 PROPER(isNeList(X:S)) -> PROPER(X:S) 0.00/0.21 PROPER(isNePal(X:S)) -> PROPER(X:S) 0.00/0.21 PROPER(isPal(X:S)) -> PROPER(X:S) 0.00/0.21 PROPER(isQid(X:S)) -> PROPER(X:S) 0.00/0.21 -> Rules: 0.00/0.21 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.21 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.21 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.21 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.21 active(__(nil,X:S)) -> mark(X:S) 0.00/0.21 active(__(X:S,nil)) -> mark(X:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.21 active(and(tt,X:S)) -> mark(X:S) 0.00/0.21 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.21 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.21 active(isList(nil)) -> mark(tt) 0.00/0.21 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.21 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.21 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isPal(nil)) -> mark(tt) 0.00/0.21 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.21 active(isQid(a)) -> mark(tt) 0.00/0.21 active(isQid(e)) -> mark(tt) 0.00/0.21 active(isQid(i)) -> mark(tt) 0.00/0.21 active(isQid(o)) -> mark(tt) 0.00/0.21 active(isQid(u)) -> mark(tt) 0.00/0.21 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.21 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.21 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.21 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.21 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.21 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.21 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.21 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.21 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.21 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.21 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.21 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.21 proper(a) -> ok(a) 0.00/0.21 proper(e) -> ok(e) 0.00/0.21 proper(i) -> ok(i) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 proper(o) -> ok(o) 0.00/0.21 proper(tt) -> ok(tt) 0.00/0.21 proper(u) -> ok(u) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 ->Projection: 0.00/0.21 pi(PROPER) = 1 0.00/0.21 0.00/0.21 Problem 1.9: 0.00/0.21 0.00/0.21 SCC Processor: 0.00/0.21 -> Pairs: 0.00/0.21 Empty 0.00/0.21 -> Rules: 0.00/0.21 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.21 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.21 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.21 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.21 active(__(nil,X:S)) -> mark(X:S) 0.00/0.21 active(__(X:S,nil)) -> mark(X:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.21 active(and(tt,X:S)) -> mark(X:S) 0.00/0.21 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.21 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.21 active(isList(nil)) -> mark(tt) 0.00/0.21 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.21 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.21 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isPal(nil)) -> mark(tt) 0.00/0.21 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.21 active(isQid(a)) -> mark(tt) 0.00/0.21 active(isQid(e)) -> mark(tt) 0.00/0.21 active(isQid(i)) -> mark(tt) 0.00/0.21 active(isQid(o)) -> mark(tt) 0.00/0.21 active(isQid(u)) -> mark(tt) 0.00/0.21 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.21 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.21 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.21 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.21 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.21 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.21 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.21 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.21 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.21 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.21 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.21 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.21 proper(a) -> ok(a) 0.00/0.21 proper(e) -> ok(e) 0.00/0.21 proper(i) -> ok(i) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 proper(o) -> ok(o) 0.00/0.21 proper(tt) -> ok(tt) 0.00/0.21 proper(u) -> ok(u) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 There is no strongly connected component 0.00/0.21 0.00/0.21 The problem is finite. 0.00/0.21 0.00/0.21 Problem 1.10: 0.00/0.21 0.00/0.21 Reduction Pairs Processor: 0.00/0.21 -> Pairs: 0.00/0.21 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.21 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.21 -> Rules: 0.00/0.21 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.21 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.21 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.21 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.21 active(__(nil,X:S)) -> mark(X:S) 0.00/0.21 active(__(X:S,nil)) -> mark(X:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.21 active(and(tt,X:S)) -> mark(X:S) 0.00/0.21 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.21 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.21 active(isList(nil)) -> mark(tt) 0.00/0.21 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.21 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.21 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isPal(nil)) -> mark(tt) 0.00/0.21 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.21 active(isQid(a)) -> mark(tt) 0.00/0.21 active(isQid(e)) -> mark(tt) 0.00/0.21 active(isQid(i)) -> mark(tt) 0.00/0.21 active(isQid(o)) -> mark(tt) 0.00/0.21 active(isQid(u)) -> mark(tt) 0.00/0.21 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.21 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.21 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.21 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.21 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.21 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.21 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.21 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.21 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.21 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.21 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.21 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.21 proper(a) -> ok(a) 0.00/0.21 proper(e) -> ok(e) 0.00/0.21 proper(i) -> ok(i) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 proper(o) -> ok(o) 0.00/0.21 proper(tt) -> ok(tt) 0.00/0.21 proper(u) -> ok(u) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 -> Usable rules: 0.00/0.21 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.21 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.21 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.21 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.21 active(__(nil,X:S)) -> mark(X:S) 0.00/0.21 active(__(X:S,nil)) -> mark(X:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.21 active(and(tt,X:S)) -> mark(X:S) 0.00/0.21 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.21 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.21 active(isList(nil)) -> mark(tt) 0.00/0.21 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.21 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.21 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isPal(nil)) -> mark(tt) 0.00/0.21 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.21 active(isQid(a)) -> mark(tt) 0.00/0.21 active(isQid(e)) -> mark(tt) 0.00/0.21 active(isQid(i)) -> mark(tt) 0.00/0.21 active(isQid(o)) -> mark(tt) 0.00/0.21 active(isQid(u)) -> mark(tt) 0.00/0.21 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.21 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.21 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.21 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.21 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.21 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.21 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.21 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.21 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.21 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.21 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.21 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.21 proper(a) -> ok(a) 0.00/0.21 proper(e) -> ok(e) 0.00/0.21 proper(i) -> ok(i) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 proper(o) -> ok(o) 0.00/0.21 proper(tt) -> ok(tt) 0.00/0.21 proper(u) -> ok(u) 0.00/0.21 ->Interpretation type: 0.00/0.21 Linear 0.00/0.21 ->Coefficients: 0.00/0.21 Natural Numbers 0.00/0.21 ->Dimension: 0.00/0.21 1 0.00/0.21 ->Bound: 0.00/0.21 2 0.00/0.21 ->Interpretation: 0.00/0.21 0.00/0.21 [__](X1,X2) = 2.X1 + X2 + 2 0.00/0.21 [active](X) = X 0.00/0.21 [and](X1,X2) = X1 + X2 + 1 0.00/0.21 [isList](X) = 2.X + 2 0.00/0.21 [isNeList](X) = 2.X + 1 0.00/0.21 [isNePal](X) = 2.X + 1 0.00/0.21 [isPal](X) = 2.X + 2 0.00/0.21 [isQid](X) = 2.X 0.00/0.21 [proper](X) = X 0.00/0.21 [top](X) = 0 0.00/0.21 [a] = 2 0.00/0.21 [e] = 2 0.00/0.21 [fSNonEmpty] = 0 0.00/0.21 [i] = 2 0.00/0.21 [mark](X) = X + 1 0.00/0.21 [nil] = 2 0.00/0.21 [o] = 2 0.00/0.21 [ok](X) = X 0.00/0.21 [tt] = 2 0.00/0.21 [u] = 2 0.00/0.21 [__#](X1,X2) = 0 0.00/0.21 [ACTIVE](X) = 0 0.00/0.21 [AND](X1,X2) = 0 0.00/0.21 [ISLIST](X) = 0 0.00/0.21 [ISNELIST](X) = 0 0.00/0.21 [ISNEPAL](X) = 0 0.00/0.21 [ISPAL](X) = 0 0.00/0.21 [ISQID](X) = 0 0.00/0.21 [PROPER](X) = 0 0.00/0.21 [TOP](X) = 2.X 0.00/0.21 0.00/0.21 Problem 1.10: 0.00/0.21 0.00/0.21 SCC Processor: 0.00/0.21 -> Pairs: 0.00/0.21 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.21 -> Rules: 0.00/0.21 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.21 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.21 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.21 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.21 active(__(nil,X:S)) -> mark(X:S) 0.00/0.21 active(__(X:S,nil)) -> mark(X:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.21 active(and(tt,X:S)) -> mark(X:S) 0.00/0.21 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.21 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.21 active(isList(nil)) -> mark(tt) 0.00/0.21 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.21 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.21 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isPal(nil)) -> mark(tt) 0.00/0.21 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.21 active(isQid(a)) -> mark(tt) 0.00/0.21 active(isQid(e)) -> mark(tt) 0.00/0.21 active(isQid(i)) -> mark(tt) 0.00/0.21 active(isQid(o)) -> mark(tt) 0.00/0.21 active(isQid(u)) -> mark(tt) 0.00/0.21 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.21 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.21 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.21 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.21 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.21 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.21 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.21 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.21 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.21 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.21 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.21 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.21 proper(a) -> ok(a) 0.00/0.21 proper(e) -> ok(e) 0.00/0.21 proper(i) -> ok(i) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 proper(o) -> ok(o) 0.00/0.21 proper(tt) -> ok(tt) 0.00/0.21 proper(u) -> ok(u) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 ->->Cycle: 0.00/0.21 ->->-> Pairs: 0.00/0.21 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.21 ->->-> Rules: 0.00/0.21 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.21 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.21 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.21 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.21 active(__(nil,X:S)) -> mark(X:S) 0.00/0.21 active(__(X:S,nil)) -> mark(X:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.21 active(and(tt,X:S)) -> mark(X:S) 0.00/0.21 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.21 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.21 active(isList(nil)) -> mark(tt) 0.00/0.21 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.21 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.21 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isPal(nil)) -> mark(tt) 0.00/0.21 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.21 active(isQid(a)) -> mark(tt) 0.00/0.21 active(isQid(e)) -> mark(tt) 0.00/0.21 active(isQid(i)) -> mark(tt) 0.00/0.21 active(isQid(o)) -> mark(tt) 0.00/0.21 active(isQid(u)) -> mark(tt) 0.00/0.21 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.21 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.21 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.21 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.21 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.21 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.21 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.21 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.21 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.21 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.21 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.21 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.21 proper(a) -> ok(a) 0.00/0.21 proper(e) -> ok(e) 0.00/0.21 proper(i) -> ok(i) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 proper(o) -> ok(o) 0.00/0.21 proper(tt) -> ok(tt) 0.00/0.21 proper(u) -> ok(u) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 0.00/0.21 Problem 1.10: 0.00/0.21 0.00/0.21 Reduction Pairs Processor: 0.00/0.21 -> Pairs: 0.00/0.21 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.21 -> Rules: 0.00/0.21 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.21 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.21 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.21 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.21 active(__(nil,X:S)) -> mark(X:S) 0.00/0.21 active(__(X:S,nil)) -> mark(X:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.21 active(and(tt,X:S)) -> mark(X:S) 0.00/0.21 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.21 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.21 active(isList(nil)) -> mark(tt) 0.00/0.21 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.21 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.21 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isPal(nil)) -> mark(tt) 0.00/0.21 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.21 active(isQid(a)) -> mark(tt) 0.00/0.21 active(isQid(e)) -> mark(tt) 0.00/0.21 active(isQid(i)) -> mark(tt) 0.00/0.21 active(isQid(o)) -> mark(tt) 0.00/0.21 active(isQid(u)) -> mark(tt) 0.00/0.21 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.21 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.21 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.21 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.21 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.21 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.21 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.21 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.21 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.21 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.21 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.21 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.21 proper(a) -> ok(a) 0.00/0.21 proper(e) -> ok(e) 0.00/0.21 proper(i) -> ok(i) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 proper(o) -> ok(o) 0.00/0.21 proper(tt) -> ok(tt) 0.00/0.21 proper(u) -> ok(u) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 -> Usable rules: 0.00/0.21 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.21 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.21 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.21 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.21 active(__(nil,X:S)) -> mark(X:S) 0.00/0.21 active(__(X:S,nil)) -> mark(X:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.21 active(and(tt,X:S)) -> mark(X:S) 0.00/0.21 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.21 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.21 active(isList(nil)) -> mark(tt) 0.00/0.21 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.21 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.21 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isPal(nil)) -> mark(tt) 0.00/0.21 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.21 active(isQid(a)) -> mark(tt) 0.00/0.21 active(isQid(e)) -> mark(tt) 0.00/0.21 active(isQid(i)) -> mark(tt) 0.00/0.21 active(isQid(o)) -> mark(tt) 0.00/0.21 active(isQid(u)) -> mark(tt) 0.00/0.21 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.21 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.21 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.21 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.21 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.21 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.21 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.21 ->Interpretation type: 0.00/0.21 Linear 0.00/0.21 ->Coefficients: 0.00/0.21 Natural Numbers 0.00/0.21 ->Dimension: 0.00/0.21 1 0.00/0.21 ->Bound: 0.00/0.21 2 0.00/0.21 ->Interpretation: 0.00/0.21 0.00/0.21 [__](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.21 [active](X) = 2.X 0.00/0.21 [and](X1,X2) = X1 + 2.X2 0.00/0.21 [isList](X) = 2.X + 2 0.00/0.21 [isNeList](X) = 2.X + 2 0.00/0.21 [isNePal](X) = 2.X + 2 0.00/0.21 [isPal](X) = 2.X + 2 0.00/0.21 [isQid](X) = 2.X + 1 0.00/0.21 [proper](X) = 0 0.00/0.21 [top](X) = 0 0.00/0.21 [a] = 2 0.00/0.21 [e] = 2 0.00/0.21 [fSNonEmpty] = 0 0.00/0.21 [i] = 1 0.00/0.21 [mark](X) = 0 0.00/0.21 [nil] = 2 0.00/0.21 [o] = 2 0.00/0.21 [ok](X) = 2.X + 2 0.00/0.21 [tt] = 0 0.00/0.21 [u] = 2 0.00/0.21 [__#](X1,X2) = 0 0.00/0.21 [ACTIVE](X) = 0 0.00/0.21 [AND](X1,X2) = 0 0.00/0.21 [ISLIST](X) = 0 0.00/0.21 [ISNELIST](X) = 0 0.00/0.21 [ISNEPAL](X) = 0 0.00/0.21 [ISPAL](X) = 0 0.00/0.21 [ISQID](X) = 0 0.00/0.21 [PROPER](X) = 0 0.00/0.21 [TOP](X) = 2.X 0.00/0.21 0.00/0.21 Problem 1.10: 0.00/0.21 0.00/0.21 SCC Processor: 0.00/0.21 -> Pairs: 0.00/0.21 Empty 0.00/0.21 -> Rules: 0.00/0.21 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S)) 0.00/0.21 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S)) 0.00/0.21 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S)) 0.00/0.21 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 0.00/0.21 active(__(nil,X:S)) -> mark(X:S) 0.00/0.21 active(__(X:S,nil)) -> mark(X:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S) 0.00/0.21 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S)) 0.00/0.21 active(and(tt,X:S)) -> mark(X:S) 0.00/0.21 active(and(X1:S,X2:S)) -> and(active(X1:S),X2:S) 0.00/0.21 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S))) 0.00/0.21 active(isList(nil)) -> mark(tt) 0.00/0.21 active(isList(V:S)) -> mark(isNeList(V:S)) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S))) 0.00/0.21 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S))) 0.00/0.21 active(isNeList(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S))) 0.00/0.21 active(isNePal(V:S)) -> mark(isQid(V:S)) 0.00/0.21 active(isPal(nil)) -> mark(tt) 0.00/0.21 active(isPal(V:S)) -> mark(isNePal(V:S)) 0.00/0.21 active(isQid(a)) -> mark(tt) 0.00/0.21 active(isQid(e)) -> mark(tt) 0.00/0.21 active(isQid(i)) -> mark(tt) 0.00/0.21 active(isQid(o)) -> mark(tt) 0.00/0.21 active(isQid(u)) -> mark(tt) 0.00/0.21 and(mark(X1:S),X2:S) -> mark(and(X1:S,X2:S)) 0.00/0.21 and(ok(X1:S),ok(X2:S)) -> ok(and(X1:S,X2:S)) 0.00/0.21 isList(ok(X:S)) -> ok(isList(X:S)) 0.00/0.21 isNeList(ok(X:S)) -> ok(isNeList(X:S)) 0.00/0.21 isNePal(ok(X:S)) -> ok(isNePal(X:S)) 0.00/0.21 isPal(ok(X:S)) -> ok(isPal(X:S)) 0.00/0.21 isQid(ok(X:S)) -> ok(isQid(X:S)) 0.00/0.21 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(and(X1:S,X2:S)) -> and(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(isList(X:S)) -> isList(proper(X:S)) 0.00/0.21 proper(isNeList(X:S)) -> isNeList(proper(X:S)) 0.00/0.21 proper(isNePal(X:S)) -> isNePal(proper(X:S)) 0.00/0.21 proper(isPal(X:S)) -> isPal(proper(X:S)) 0.00/0.21 proper(isQid(X:S)) -> isQid(proper(X:S)) 0.00/0.21 proper(a) -> ok(a) 0.00/0.21 proper(e) -> ok(e) 0.00/0.21 proper(i) -> ok(i) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 proper(o) -> ok(o) 0.00/0.21 proper(tt) -> ok(tt) 0.00/0.21 proper(u) -> ok(u) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 There is no strongly connected component 0.00/0.21 0.00/0.21 The problem is finite. 0.00/0.21 EOF