YES Problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [1] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [0] [tt] = [0] [0], [0] [nil] = [0] [0], [1 0 0] [mark](x0) = [1 0 0]x0 [0 0 0] , [1 0 0] [active](x0) = [1 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(__(__(X,Y),Z)) = [1 0 0]X + [1 0 0]Y + [1 0 0]Z >= [1 0 0]X + [1 0 0]Y + [1 0 0]Z = mark(__(X,__(Y,Z))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] active(__(X,nil())) = [1 0 0]X >= [1 0 0]X = mark(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] active(__(nil(),X)) = [1 0 0]X >= [1 0 0]X = mark(X) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] active(and(tt(),X)) = [1 0 0]X + [1] >= [1 0 0]X = mark(X) [0 0 0] [0] [0 0 0] [2 0 0] [1 0 0] [0] active(isNePal(__(I,__(P,I)))) = [2 0 0]I + [1 0 0]P >= [0] = mark(tt()) [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] mark(__(X1,X2)) = [1 0 0]X1 + [1 0 0]X2 >= [1 0 0]X1 + [1 0 0]X2 = active(__(mark(X1),mark(X2))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] mark(and(X1,X2)) = [1 0 0]X1 + [1 0 0]X2 + [1] >= [1 0 0]X1 + [1 0 0]X2 + [1] = active(and(mark(X1),X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [0] [0] mark(tt()) = [0] >= [0] = active(tt()) [0] [0] [1 0 0] [1 0 0] mark(isNePal(X)) = [1 0 0]X >= [1 0 0]X = active(isNePal(mark(X))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] and(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = and(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] and(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = and(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] and(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = and(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] and(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = and(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] isNePal(mark(X)) = [0 0 0]X >= [0 0 0]X = isNePal(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNePal(active(X)) = [0 0 0]X >= [0 0 0]X = isNePal(X) [0 0 0] [0 0 0] problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [tt] = [0] [0], [1] [nil] = [0] [0], [1 0 0] [0] [mark](x0) = [0 0 0]x0 + [1] [1 0 0] [0], [1 0 0] [0] [active](x0) = [0 0 0]x0 + [1] [1 0 0] [0], [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [0] active(__(__(X,Y),Z)) = [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [1] >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [1] = mark(__(X,__(Y,Z))) [1 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1] [1 0 0] [0] active(__(X,nil())) = [0 0 0]X + [1] >= [0 0 0]X + [1] = mark(X) [1 0 0] [1] [1 0 0] [0] [1 0 0] [1] [1 0 0] [0] active(__(nil(),X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = mark(X) [1 0 0] [1] [1 0 0] [0] [2 0 0] [1 0 0] [0] [0] active(isNePal(__(I,__(P,I)))) = [0 0 0]I + [0 0 0]P + [1] >= [1] = mark(tt()) [2 0 0] [1 0 0] [0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] mark(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = active(__(mark(X1),mark(X2))) [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] [1] [1] mark(nil()) = [1] >= [1] = active(nil()) [1] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] mark(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = active(and(mark(X1),X2)) [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] [0] [0] mark(tt()) = [1] >= [1] = active(tt()) [0] [0] [1 0 0] [0] [1 0 0] [0] mark(isNePal(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = active(isNePal(mark(X))) [1 0 0] [0] [1 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] and(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] and(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] and(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] and(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNePal(mark(X)) = [0 0 0]X >= [0 0 0]X = isNePal(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNePal(active(X)) = [0 0 0]X >= [0 0 0]X = isNePal(X) [0 0 0] [0 0 0] problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) DP Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(nil()) -> active#(nil()) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> isNePal#(mark(X)) mark#(isNePal(X)) -> active#(isNePal(mark(X))) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) isNePal#(mark(X)) -> isNePal#(X) isNePal#(active(X)) -> isNePal#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) TDG Processor: DPs: active#(__(__(X,Y),Z)) -> __#(Y,Z) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(nil()) -> active#(nil()) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> isNePal#(mark(X)) mark#(isNePal(X)) -> active#(isNePal(mark(X))) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) isNePal#(mark(X)) -> isNePal#(X) isNePal#(active(X)) -> isNePal#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) graph: isNePal#(mark(X)) -> isNePal#(X) -> isNePal#(active(X)) -> isNePal#(X) isNePal#(mark(X)) -> isNePal#(X) -> isNePal#(mark(X)) -> isNePal#(X) isNePal#(active(X)) -> isNePal#(X) -> isNePal#(active(X)) -> isNePal#(X) isNePal#(active(X)) -> isNePal#(X) -> isNePal#(mark(X)) -> isNePal#(X) and#(mark(X1),X2) -> and#(X1,X2) -> and#(X1,active(X2)) -> and#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) -> and#(active(X1),X2) -> and#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) -> and#(X1,mark(X2)) -> and#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) -> and#(mark(X1),X2) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) -> and#(X1,active(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) -> and#(active(X1),X2) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) -> and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) -> and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) -> and#(X1,active(X2)) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) -> and#(active(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) -> and#(X1,mark(X2)) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) -> and#(mark(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) -> and#(X1,active(X2)) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) -> and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) -> and#(X1,mark(X2)) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) -> and#(mark(X1),X2) -> and#(X1,X2) mark#(isNePal(X)) -> isNePal#(mark(X)) -> isNePal#(active(X)) -> isNePal#(X) mark#(isNePal(X)) -> isNePal#(mark(X)) -> isNePal#(mark(X)) -> isNePal#(X) mark#(isNePal(X)) -> mark#(X) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(isNePal(X)) -> mark#(X) -> mark#(isNePal(X)) -> isNePal#(mark(X)) mark#(isNePal(X)) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) mark#(isNePal(X)) -> mark#(X) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isNePal(X)) -> mark#(X) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(isNePal(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(isNePal(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(isNePal(X)) -> mark#(X) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(isNePal(X)) -> mark#(X) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(isNePal(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) mark#(isNePal(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) mark#(and(X1,X2)) -> and#(mark(X1),X2) -> and#(X1,active(X2)) -> and#(X1,X2) mark#(and(X1,X2)) -> and#(mark(X1),X2) -> and#(active(X1),X2) -> and#(X1,X2) mark#(and(X1,X2)) -> and#(mark(X1),X2) -> and#(X1,mark(X2)) -> and#(X1,X2) mark#(and(X1,X2)) -> and#(mark(X1),X2) -> and#(mark(X1),X2) -> and#(X1,X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> isNePal#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(and(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) mark#(tt()) -> active#(tt()) -> active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) mark#(tt()) -> active#(tt()) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(tt()) -> active#(tt()) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) mark#(tt()) -> active#(tt()) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) mark#(nil()) -> active#(nil()) -> active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) mark#(nil()) -> active#(nil()) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(nil()) -> active#(nil()) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) mark#(nil()) -> active#(nil()) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isNePal(X)) -> isNePal#(mark(X)) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isNePal(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X2) -> mark#(tt()) -> active#(tt()) mark#(__(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(__(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(__(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X2) -> mark#(nil()) -> active#(nil()) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> isNePal#(mark(X)) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(__(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(__(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(__(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) -> __#(X1,active(X2)) -> __#(X1,X2) mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) -> __#(active(X1),X2) -> __#(X1,X2) mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) -> __#(X1,mark(X2)) -> __#(X1,X2) mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) -> __#(mark(X1),X2) -> __#(X1,X2) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(__(__(X,Y),Z)) -> __#(Y,Z) __#(mark(X1),X2) -> __#(X1,X2) -> __#(X1,active(X2)) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) -> __#(active(X1),X2) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(mark(X1),X2) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) -> __#(X1,active(X2)) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) -> __#(active(X1),X2) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(X1,active(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(active(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) -> __#(X1,active(X2)) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) -> __#(active(X1),X2) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) -> __#(X1,mark(X2)) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) -> __#(mark(X1),X2) -> __#(X1,X2) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(isNePal(X)) -> isNePal#(mark(X)) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(isNePal(X)) -> mark#(X) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(tt()) -> active#(tt()) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(and(X1,X2)) -> mark#(X1) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(nil()) -> active#(nil()) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(__(X1,X2)) -> mark#(X1) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(__(X1,X2)) -> mark#(X2) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(isNePal(X)) -> isNePal#(mark(X)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(isNePal(X)) -> mark#(X) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(tt()) -> active#(tt()) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(and(X1,X2)) -> mark#(X1) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(nil()) -> active#(nil()) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(__(X1,X2)) -> __#(mark(X1),mark(X2)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(__(X1,X2)) -> mark#(X1) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(__(X1,X2)) -> mark#(X2) active#(__(__(X,Y),Z)) -> __#(Y,Z) -> __#(X1,active(X2)) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(Y,Z) -> __#(active(X1),X2) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(Y,Z) -> __#(X1,mark(X2)) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(Y,Z) -> __#(mark(X1),X2) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) -> __#(X1,active(X2)) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) -> __#(active(X1),X2) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) -> __#(X1,mark(X2)) -> __#(X1,X2) active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z)) -> __#(mark(X1),X2) -> __#(X1,X2) SCC Processor: #sccs: 4 #rules: 21 #arcs: 146/676 DPs: mark#(isNePal(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(nil()) -> active#(nil()) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(isNePal(X)) -> active#(isNePal(mark(X))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) EDG Processor: DPs: mark#(isNePal(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(nil()) -> active#(nil()) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(isNePal(X)) -> active#(isNePal(mark(X))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) graph: mark#(isNePal(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2) mark#(isNePal(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1) mark#(isNePal(X)) -> mark#(X) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(isNePal(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(isNePal(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(isNePal(X)) -> mark#(X) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isNePal(X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) mark#(isNePal(X)) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> mark#(X) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(isNePal(X)) -> active#(isNePal(mark(X))) -> active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(and(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) -> mark#(X2) -> mark#(nil()) -> active#(nil()) mark#(__(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(__(X1,X2)) -> mark#(X2) -> mark#(tt()) -> active#(tt()) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isNePal(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X2) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X2) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) mark#(__(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(__(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> mark#(X) mark#(__(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) -> active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) active#(isNePal(__(I,__(P,I)))) -> mark#(tt()) -> mark#(tt()) -> active#(tt()) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(__(X1,X2)) -> mark#(X2) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(__(X1,X2)) -> mark#(X1) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(and(X1,X2)) -> mark#(X1) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(isNePal(X)) -> mark#(X) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) -> mark#(isNePal(X)) -> active#(isNePal(mark(X))) SCC Processor: #sccs: 1 #rules: 8 #arcs: 50/121 DPs: mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(mark(X))) active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(and(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) mark#(__(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> mark#(X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Semantic Labeling Processor: dimension: 1 usable rules: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) interpretation: [isNePal](x0) = 1, [and](x0, x1) = 0, [tt] = 0, [nil] = 0, [mark](x0) = 0, [active](x0) = x0, [__](x0, x1) = 0 labeled: usable (for model): argument filtering: pi(__) = [0,1] pi(active) = 0 pi(mark) = 0 pi(nil) = [] pi(tt) = [] pi(and) = 0 pi(isNePal) = 0 pi(active#) = 0 pi(mark#) = 0 precedence: __ > mark# ~ active# ~ isNePal ~ and ~ tt ~ nil ~ mark ~ active problem: DPs: mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(and(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Restore Modifier: DPs: mark#(isNePal(X)) -> mark#(X) mark#(isNePal(X)) -> active#(isNePal(mark(X))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(and(X1,X2)) -> mark#(X1) mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2))) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) SCC Processor: #sccs: 1 #rules: 2 #arcs: 38/25 DPs: mark#(isNePal(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {3} transitions: f650() -> 4* mark{#,0}(4) -> 3* problem: DPs: mark#(isNePal(X)) -> mark#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {1} transitions: f680() -> 2* mark{#,0}(2) -> 1* problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Qed DPs: __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) __#(X1,active(X2)) -> __#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Subterm Criterion Processor: simple projection: pi(__#) = 1 problem: DPs: __#(mark(X1),X2) -> __#(X1,X2) __#(active(X1),X2) -> __#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Subterm Criterion Processor: simple projection: pi(__#) = 0 problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Qed DPs: and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Subterm Criterion Processor: simple projection: pi(and#) = 1 problem: DPs: and#(mark(X1),X2) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Subterm Criterion Processor: simple projection: pi(and#) = 0 problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Qed DPs: isNePal#(mark(X)) -> isNePal#(X) isNePal#(active(X)) -> isNePal#(X) TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Subterm Criterion Processor: simple projection: pi(isNePal#) = 0 problem: DPs: TRS: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Qed