Input TRS: 1: topB(i,N1(x),y) -> topA(1(),T1(x),y) 2: topA(i,x,N2(y)) -> topB(0(),x,T2(y)) 3: topB(i,S1(x),y) -> topA(i,N1(x),y) 4: topA(i,x,S2(y)) -> topB(i,x,N2(y)) 5: topA(i,N1(x),T2(y)) -> topB(i,N1(x),S2(y)) 6: topA(1(),T1(x),T2(y)) -> topB(1(),T1(x),S2(y)) e1: topA(i,N1(x),y) ->= topA(1(),T1(x),y) [relative] e2: topB(i,x,N2(y)) ->= topB(0(),x,T2(y)) [relative] e3: topA(i,S1(x),y) ->= topA(i,N1(x),y) [relative] e4: topB(i,x,S2(y)) ->= topB(i,x,N2(y)) [relative] e5: topB(i,N1(x),T2(y)) ->= topB(i,N1(x),S2(y)) [relative] e6: topB(1(),T1(x),T2(y)) ->= topB(1(),T1(x),S2(y)) [relative] e7: topA(i,N1(x),y) ->= topA(i,N1(C(x)),y) [relative] e8: topB(i,x,N2(y)) ->= topB(i,x,N2(C(y))) [relative] e9: topA(i,T1(x),y) ->= topA(i,T1(x),y) [relative] e10: topB(i,x,T2(y)) ->= topB(i,x,T2(y)) [relative] e11: topB(i,x,S2(y)) ->= topB(i,x,S2(D(y))) [relative] Removing trivial relative rule e9. Removing trivial relative rule e10. Dependency Pairs: #1: # topA(i,x,N2(y)) -> # topB(0(),x,T2(y)) #2: # topA(1(),T1(x),T2(y)) -> # topB(1(),T1(x),S2(y)) #3: # topB(i,x,S2(y)) -> # topB(i,x,N2(y)) [relative] #4: # topB(i,x,N2(y)) -> # topB(i,x,N2(C(y))) [relative] #5: # topA(i,S1(x),y) -> # topA(i,N1(x),y) [relative] #6: # topB(i,N1(x),T2(y)) -> # topB(i,N1(x),S2(y)) [relative] #7: # topB(i,x,S2(y)) -> # topB(i,x,S2(D(y))) [relative] #8: # topB(1(),T1(x),T2(y)) -> # topB(1(),T1(x),S2(y)) [relative] #9: # topA(i,N1(x),y) -> # topA(i,N1(C(x)),y) [relative] #10: # topA(i,N1(x),T2(y)) -> # topB(i,N1(x),S2(y)) #11: # topB(i,S1(x),y) -> # topA(i,N1(x),y) #12: # topB(i,N1(x),y) -> # topA(1(),T1(x),y) #13: # topB(i,x,N2(y)) -> # topB(0(),x,T2(y)) [relative] #14: # topA(i,N1(x),y) -> # topA(1(),T1(x),y) [relative] #15: # topA(i,x,S2(y)) -> # topB(i,x,N2(y)) Number of SCCs: 1 SCC { #1..4 #6 #7 #9..15 } POLO(Sum)... removes: #1 #2 #10 #11 #12 #14 #15 I(1) = 1 I(T1) = 0 I(S1) = max(x1 + 9, 0) I(T2) = 0 I(# topB) = max(x1 + x2 + x3 - 2, 0) I(D) = 1 I(C) = max(x1 - 1, 0) I(0) = 0 I(# topA) = max(x1 + x2 + x3 + 1, 0) I(N2) = 0 I(N1) = 5 I(S2) = 0 USABLE RULES: { } Number of SCCs: 2 SCC { #9 } POLO(Sum)... QLPOS... QWPOpS(mSum)... Mat2b... failed.