Input TRS: 1: s(a(x)) -> s(b(x)) 2: b(b(x)) -> a(x) e1: f(s(x),y) ->= f(x,s(y)) [relative] e2: s(a(x)) ->= a(s(x)) [relative] e3: s(b(x)) ->= b(s(x)) [relative] e4: a(s(x)) ->= s(a(x)) [relative] e5: b(s(x)) ->= s(b(x)) [relative] Dependency Pairs: #1: # b(b(x)) -> # a(x) #2: # a(s(x)) -> # s(a(x)) [relative] #3: # a(s(x)) -> # a(x) [relative] #4: # f(s(x),y) -> # f(x,s(y)) [relative] #5: # f(s(x),y) -> # s(y) [relative] #6: # b(s(x)) -> # s(b(x)) [relative] #7: # b(s(x)) -> # b(x) [relative] #8: # s(a(x)) -> # a(s(x)) [relative] #9: # s(a(x)) -> # s(x) [relative] #10: # s(a(x)) -> # s(b(x)) #11: # s(a(x)) -> # b(x) #12: # s(b(x)) -> # b(s(x)) [relative] #13: # s(b(x)) -> # s(x) [relative] Number of SCCs: 2 SCC { #4 } POLO(Sum)... removes: #4 I(a) = 0 I(# a) = 0 I(s) = max(x1 + 1, 0) I(b) = 0 I(# s) = max(x1 - 1, 0) I(# f) = max(x1 + 1, 0) I(# b) = max(x1 - 1, 0) USABLE RULES: { } Number of SCCs: 1 SCC { #1..3 #6..13 } POLO(Sum)... removes: #1 #3 #7 #9 #10 #11 #13 I(a) = max(x1 + 5, 0) I(# a) = max(x1 + 1, 0) I(s) = max(x1 + 6, 0) I(b) = max(x1 + 3, 0) I(# s) = max(x1 + 2, 0) I(# f) = max(x1 + 1, 0) I(# b) = max(x1 - 1, 0) USABLE RULES: { 4 1 3 5 6 2 } Number of SCCs: 1 SCC { #2 #6 #8 #12 } POLO(Sum)... QLPOS... QWPOpS(mSum)... Mat2b... failed.