Input TRS: 1: top(ok(queue(old(x),bot()))) -> top(check(queue(x,bot()))) 2: top(ok(queue(new(x),bot()))) -> top(check(queue(x,bot()))) 3: top(ok(queue(bot(),old(x)))) -> top(check(queue(bot(),x))) 4: top(ok(queue(bot(),new(x)))) -> top(check(queue(bot(),x))) 5: top(ok(queue(old(x),old(y)))) -> top(check(queue(x,y))) 6: top(ok(queue(old(x),new(y)))) -> top(check(queue(x,y))) 7: top(ok(queue(new(x),old(y)))) -> top(check(queue(x,y))) 8: top(ok(queue(new(x),new(y)))) -> top(check(queue(x,y))) e1: top(ok(queue(old(x),y))) ->= top(check(queue(x,y))) [relative] e2: top(ok(queue(new(x),y))) ->= top(check(queue(x,y))) [relative] e3: bot() ->= new(bot()) [relative] e4: check(old(x)) ->= ok(old(x)) [relative] e5: check(new(x)) ->= new(check(x)) [relative] e6: check(queue(x,y)) ->= queue(check(x),y) [relative] e7: check(queue(x,y)) ->= queue(x,check(y)) [relative] e8: old(ok(x)) ->= ok(old(x)) [relative] e9: new(ok(x)) ->= ok(new(x)) [relative] e10: queue(ok(x),y) ->= ok(queue(x,y)) [relative] e11: queue(x,ok(y)) ->= ok(queue(x,y)) [relative] Dependency Pairs: #1: # top(ok(queue(new(x),bot()))) -> # top(check(queue(x,bot()))) #2: # top(ok(queue(old(x),new(y)))) -> # top(check(queue(x,y))) #3: # top(ok(queue(new(x),y))) -> # top(check(queue(x,y))) [relative] #4: # top(ok(queue(new(x),old(y)))) -> # top(check(queue(x,y))) #5: # top(ok(queue(old(x),y))) -> # top(check(queue(x,y))) [relative] #6: # top(ok(queue(old(x),old(y)))) -> # top(check(queue(x,y))) #7: # top(ok(queue(bot(),old(x)))) -> # top(check(queue(bot(),x))) #8: # top(ok(queue(old(x),bot()))) -> # top(check(queue(x,bot()))) #9: # top(ok(queue(new(x),new(y)))) -> # top(check(queue(x,y))) #10: # top(ok(queue(bot(),new(x)))) -> # top(check(queue(bot(),x))) Number of SCCs: 1 SCC { #1..10 } POLO(Sum)... removes: #2 #4 #5 #6 #7 #8 I(new) = max(x1, 0) I(top) = 0 I(bot) = 1 I(queue) = max(x1 + x2 + 1, 0) I(check) = max(x1 + 3, 0) I(ok) = max(x1 + 3, 0) I(# top) = max(x1 - 5, 0) I(old) = max(x1 + 2, 0) Number of SCCs: 1 SCC { #1 #3 #9 #10 } POLO(Sum)... QLPOS... QWPOpS(mSum)... Mat2b... failed.