YES(?,O(n^1)) 0.17/0.61 YES(?,O(n^1)) 0.17/0.62 0.17/0.62 Problem: 0.17/0.62 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) 0.17/0.62 active(__(X,nil())) -> mark(X) 0.17/0.62 active(__(nil(),X)) -> mark(X) 0.17/0.62 active(and(tt(),X)) -> mark(X) 0.17/0.62 active(isNePal(__(I,__(P,I)))) -> mark(tt()) 0.17/0.62 active(__(X1,X2)) -> __(active(X1),X2) 0.17/0.62 active(__(X1,X2)) -> __(X1,active(X2)) 0.17/0.62 active(and(X1,X2)) -> and(active(X1),X2) 0.17/0.62 active(isNePal(X)) -> isNePal(active(X)) 0.17/0.62 __(mark(X1),X2) -> mark(__(X1,X2)) 0.17/0.62 __(X1,mark(X2)) -> mark(__(X1,X2)) 0.17/0.62 and(mark(X1),X2) -> mark(and(X1,X2)) 0.17/0.62 isNePal(mark(X)) -> mark(isNePal(X)) 0.17/0.62 proper(__(X1,X2)) -> __(proper(X1),proper(X2)) 0.17/0.62 proper(nil()) -> ok(nil()) 0.17/0.62 proper(and(X1,X2)) -> and(proper(X1),proper(X2)) 0.17/0.62 proper(tt()) -> ok(tt()) 0.17/0.62 proper(isNePal(X)) -> isNePal(proper(X)) 0.17/0.62 __(ok(X1),ok(X2)) -> ok(__(X1,X2)) 0.17/0.62 and(ok(X1),ok(X2)) -> ok(and(X1,X2)) 0.17/0.62 isNePal(ok(X)) -> ok(isNePal(X)) 0.17/0.62 top(mark(X)) -> top(proper(X)) 0.17/0.62 top(ok(X)) -> top(active(X)) 0.17/0.62 0.17/0.62 Proof: 0.17/0.62 Bounds Processor: 0.17/0.62 bound: 2 0.17/0.62 enrichment: match 0.17/0.62 automaton: 0.17/0.62 final states: {25,24,10,9,8,7,6,5} 0.17/0.62 transitions: 0.17/0.62 active0(25) -> 5* 0.17/0.62 active0(2) -> 5* 0.17/0.62 active0(4) -> 5* 0.17/0.62 active0(26) -> 5* 0.17/0.62 active0(1) -> 5* 0.17/0.62 active0(3) -> 5* 0.17/0.62 __0(3,1) -> 6* 0.17/0.62 __0(3,3) -> 6* 0.17/0.62 __0(2,26) -> 6* 0.17/0.62 __0(4,2) -> 6* 0.17/0.62 __0(4,4) -> 6* 0.17/0.62 __0(3,25) -> 6* 0.17/0.62 __0(25,1) -> 6* 0.17/0.62 __0(25,3) -> 6* 0.17/0.62 __0(4,26) -> 6* 0.17/0.62 __0(26,2) -> 6* 0.17/0.62 __0(26,4) -> 6* 0.17/0.62 __0(25,25) -> 6* 0.17/0.62 __0(1,2) -> 6* 0.17/0.62 __0(1,4) -> 6* 0.17/0.62 __0(2,1) -> 6* 0.17/0.62 __0(26,26) -> 6* 0.17/0.62 __0(2,3) -> 6* 0.17/0.62 __0(1,26) -> 6* 0.17/0.62 __0(3,2) -> 6* 0.17/0.62 __0(3,4) -> 6* 0.17/0.62 __0(2,25) -> 6* 0.17/0.62 __0(4,1) -> 6* 0.17/0.62 __0(4,3) -> 6* 0.17/0.62 __0(3,26) -> 6* 0.17/0.62 __0(25,2) -> 6* 0.17/0.62 __0(25,4) -> 6* 0.17/0.62 __0(4,25) -> 6* 0.17/0.62 __0(26,1) -> 6* 0.17/0.62 __0(26,3) -> 6* 0.17/0.62 __0(1,1) -> 6* 0.17/0.62 __0(25,26) -> 6* 0.17/0.62 __0(1,3) -> 6* 0.17/0.62 __0(26,25) -> 6* 0.17/0.62 __0(2,2) -> 6* 0.17/0.62 __0(2,4) -> 6* 0.17/0.62 __0(1,25) -> 6* 0.17/0.62 mark0(25) -> 1* 0.17/0.62 mark0(2) -> 1* 0.17/0.62 mark0(4) -> 1* 0.17/0.62 mark0(26) -> 1* 0.17/0.62 mark0(1) -> 1* 0.17/0.62 mark0(3) -> 1* 0.17/0.62 nil0() -> 2* 0.17/0.62 and0(3,1) -> 7* 0.17/0.62 and0(3,3) -> 7* 0.17/0.62 and0(2,26) -> 7* 0.17/0.62 and0(4,2) -> 7* 0.17/0.62 and0(4,4) -> 7* 0.17/0.62 and0(3,25) -> 7* 0.17/0.62 and0(25,1) -> 7* 0.17/0.62 and0(25,3) -> 7* 0.17/0.62 and0(4,26) -> 7* 0.17/0.62 and0(26,2) -> 7* 0.17/0.62 and0(26,4) -> 7* 0.17/0.62 and0(25,25) -> 7* 0.17/0.62 and0(1,2) -> 7* 0.17/0.62 and0(1,4) -> 7* 0.17/0.62 and0(2,1) -> 7* 0.17/0.62 and0(26,26) -> 7* 0.17/0.62 and0(2,3) -> 7* 0.17/0.62 and0(1,26) -> 7* 0.17/0.62 and0(3,2) -> 7* 0.17/0.62 and0(3,4) -> 7* 0.17/0.62 and0(2,25) -> 7* 0.17/0.62 and0(4,1) -> 7* 0.17/0.62 and0(4,3) -> 7* 0.17/0.62 and0(3,26) -> 7* 0.17/0.62 and0(25,2) -> 7* 0.17/0.62 and0(25,4) -> 7* 0.17/0.62 and0(4,25) -> 7* 0.17/0.62 and0(26,1) -> 7* 0.17/0.62 and0(26,3) -> 7* 0.17/0.62 and0(1,1) -> 7* 0.17/0.62 and0(25,26) -> 7* 0.17/0.62 and0(1,3) -> 7* 0.17/0.62 and0(26,25) -> 7* 0.17/0.62 and0(2,2) -> 7* 0.17/0.62 and0(2,4) -> 7* 0.17/0.62 and0(1,25) -> 7* 0.17/0.62 tt0() -> 3* 0.17/0.62 isNePal0(25) -> 8* 0.17/0.62 isNePal0(2) -> 8* 0.17/0.62 isNePal0(4) -> 8* 0.17/0.62 isNePal0(26) -> 8* 0.17/0.62 isNePal0(1) -> 8* 0.17/0.62 isNePal0(3) -> 8* 0.17/0.62 proper0(25) -> 9* 0.17/0.62 proper0(2) -> 9* 0.17/0.62 proper0(4) -> 9* 0.17/0.62 proper0(26) -> 9* 0.17/0.62 proper0(1) -> 9* 0.17/0.62 proper0(3) -> 9* 0.17/0.62 ok0(25) -> 4* 0.17/0.62 ok0(2) -> 4* 0.17/0.62 ok0(4) -> 4* 0.17/0.62 ok0(26) -> 4* 0.17/0.62 ok0(1) -> 4* 0.17/0.62 ok0(3) -> 4* 0.17/0.62 top0(25) -> 10* 0.17/0.62 top0(2) -> 10* 0.17/0.62 top0(4) -> 10* 0.17/0.62 top0(26) -> 10* 0.17/0.62 top0(1) -> 10* 0.17/0.62 top0(3) -> 10* 0.17/0.62 top1(25) -> 10* 0.17/0.62 top1(24) -> 10* 0.17/0.62 top1(9) -> 10* 0.17/0.62 active1(25) -> 5,24* 0.17/0.62 active1(2) -> 24*,5,9 0.17/0.62 active1(4) -> 24*,5,9 0.17/0.62 active1(26) -> 5,24* 0.17/0.62 active1(1) -> 24*,5,9 0.17/0.62 active1(3) -> 24*,5,9 0.17/0.62 proper1(25) -> 9* 0.17/0.62 proper1(2) -> 9* 0.17/0.62 proper1(4) -> 9* 0.17/0.62 proper1(26) -> 9* 0.17/0.62 proper1(1) -> 9* 0.17/0.62 proper1(3) -> 9* 0.17/0.62 ok1(7) -> 7* 0.17/0.62 ok1(2) -> 25*,4,9 0.17/0.62 ok1(26) -> 4,25* 0.17/0.62 ok1(6) -> 6* 0.17/0.62 ok1(8) -> 8* 0.17/0.62 isNePal1(25) -> 8* 0.17/0.62 isNePal1(2) -> 8* 0.17/0.62 isNePal1(4) -> 8* 0.17/0.62 isNePal1(26) -> 8* 0.17/0.62 isNePal1(1) -> 8* 0.17/0.62 isNePal1(3) -> 8* 0.17/0.62 and1(3,1) -> 7* 0.17/0.62 and1(3,3) -> 7* 0.17/0.62 and1(2,26) -> 7* 0.17/0.62 and1(4,2) -> 7* 0.17/0.62 and1(4,4) -> 7* 0.17/0.62 and1(3,25) -> 7* 0.17/0.62 and1(25,1) -> 7* 0.17/0.62 and1(25,3) -> 7* 0.17/0.62 and1(4,26) -> 7* 0.17/0.62 and1(26,2) -> 7* 0.17/0.62 and1(26,4) -> 7* 0.17/0.62 and1(25,25) -> 7* 0.17/0.62 and1(1,2) -> 7* 0.17/0.62 and1(1,4) -> 7* 0.17/0.62 and1(2,1) -> 7* 0.17/0.62 and1(26,26) -> 7* 0.17/0.62 and1(2,3) -> 7* 0.17/0.62 and1(1,26) -> 7* 0.17/0.62 and1(3,2) -> 7* 0.17/0.62 and1(3,4) -> 7* 0.17/0.62 and1(2,25) -> 7* 0.17/0.62 and1(4,1) -> 7* 0.17/0.62 and1(4,3) -> 7* 0.17/0.62 and1(3,26) -> 7* 0.17/0.62 and1(25,2) -> 7* 0.17/0.62 and1(25,4) -> 7* 0.17/0.62 and1(4,25) -> 7* 0.17/0.62 and1(26,1) -> 7* 0.17/0.62 and1(26,3) -> 7* 0.17/0.62 and1(1,1) -> 7* 0.17/0.62 and1(25,26) -> 7* 0.17/0.62 and1(1,3) -> 7* 0.17/0.62 and1(26,25) -> 7* 0.17/0.62 and1(2,2) -> 7* 0.17/0.62 and1(2,4) -> 7* 0.17/0.62 and1(1,25) -> 7* 0.17/0.62 __1(3,1) -> 6* 0.17/0.62 __1(3,3) -> 6* 0.17/0.62 __1(2,26) -> 6* 0.17/0.62 __1(4,2) -> 6* 0.17/0.62 __1(4,4) -> 6* 0.17/0.62 __1(3,25) -> 6* 0.17/0.62 __1(25,1) -> 6* 0.17/0.62 __1(25,3) -> 6* 0.17/0.62 __1(4,26) -> 6* 0.17/0.62 __1(26,2) -> 6* 0.17/0.62 __1(26,4) -> 6* 0.17/0.62 __1(25,25) -> 6* 0.17/0.62 __1(1,2) -> 6* 0.17/0.62 __1(1,4) -> 6* 0.17/0.62 __1(2,1) -> 6* 0.17/0.62 __1(26,26) -> 6* 0.17/0.62 __1(2,3) -> 6* 0.17/0.62 __1(1,26) -> 6* 0.17/0.62 __1(3,2) -> 6* 0.17/0.62 __1(3,4) -> 6* 0.17/0.62 __1(2,25) -> 6* 0.17/0.62 __1(4,1) -> 6* 0.17/0.62 __1(4,3) -> 6* 0.17/0.62 __1(3,26) -> 6* 0.17/0.62 __1(25,2) -> 6* 0.17/0.62 __1(25,4) -> 6* 0.17/0.62 __1(4,25) -> 6* 0.17/0.62 __1(26,1) -> 6* 0.17/0.62 __1(26,3) -> 6* 0.17/0.62 __1(1,1) -> 6* 0.17/0.62 __1(25,26) -> 6* 0.17/0.62 __1(1,3) -> 6* 0.17/0.62 __1(26,25) -> 6* 0.17/0.62 __1(2,2) -> 6* 0.17/0.62 __1(2,4) -> 6* 0.17/0.62 __1(1,25) -> 6* 0.17/0.62 tt1() -> 26*,3,2 0.17/0.62 nil1() -> 2* 0.17/0.62 mark1(7) -> 7* 0.17/0.62 mark1(6) -> 6* 0.17/0.62 mark1(8) -> 8* 0.17/0.62 ok2(7) -> 7* 0.17/0.62 ok2(2) -> 4,25*,9 0.17/0.62 ok2(26) -> 4,25* 0.17/0.62 ok2(6) -> 6* 0.17/0.62 ok2(8) -> 8* 0.17/0.62 isNePal2(2) -> 8* 0.17/0.62 isNePal2(26) -> 8* 0.17/0.62 and2(2,26) -> 7* 0.17/0.62 and2(26,2) -> 7* 0.17/0.62 and2(26,26) -> 7* 0.17/0.62 and2(2,2) -> 7* 0.17/0.62 __2(2,26) -> 6* 0.17/0.62 __2(26,2) -> 6* 0.17/0.62 __2(26,26) -> 6* 0.17/0.62 __2(2,2) -> 6* 0.17/0.62 tt2() -> 3,26*,2 0.17/0.62 nil2() -> 2* 0.17/0.62 top2(5) -> 10* 0.17/0.62 top2(24) -> 10* 0.17/0.62 active2(2) -> 9,24*,5 0.17/0.62 active2(26) -> 24*,5 0.17/0.62 problem: 0.17/0.62 0.17/0.62 Qed 0.17/0.62 EOF