MAYBE Input TRS: 1: f(true(),xs) -> f(isList(xs),append(cons(a(),nil()),xs)) 2: isList(nil()) -> true() 3: isList(cons(x,xs)) -> isList(xs) 4: append(nil(),ys) -> ys 5: append(cons(x,xs),ys) -> cons(x,append(xs,ys)) Number of strict rules: 5 Direct POLO(bPol) ... failed. Uncurrying append 1: f(true(),xs) -> f(isList(xs),append^1_cons(a(),nil(),xs)) 2: isList(nil()) -> true() 3: isList(cons(x,xs)) -> isList(xs) 4: append^1_nil(ys) -> ys 5: append^1_cons(x,xs,ys) -> cons(x,append(xs,ys)) 6: append(cons(_1,_2),_3) ->= append^1_cons(_1,_2,_3) 7: append(nil(),_1) ->= append^1_nil(_1) Number of strict rules: 5 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #append(cons(_1,_2),_3) ->? #append^1_cons(_1,_2,_3) #2: #append(nil(),_1) ->? #append^1_nil(_1) #3: #append^1_cons(x,xs,ys) -> #append(xs,ys) #4: #isList(cons(x,xs)) -> #isList(xs) #5: #f(true(),xs) -> #f(isList(xs),append^1_cons(a(),nil(),xs)) #6: #f(true(),xs) -> #isList(xs) #7: #f(true(),xs) -> #append^1_cons(a(),nil(),xs) Number of SCCs: 3, DPs: 4 SCC { #4 } POLO(Sum)... succeeded. a w: 0 append^1_cons w: 0 #append w: 0 #append^1_cons w: 0 #append^1_nil w: 0 true w: 0 f w: 0 append w: 0 isList w: 0 nil w: 0 #f w: 0 #isList w: x1 cons w: x2 + 1 append^1_nil w: 0 USABLE RULES: { } Removed DPs: #4 Number of SCCs: 2, DPs: 3 SCC { #5 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. Finding a loop... failed.