Input TRS: 1: Tl(O(x),y) -> Wr(check(x),y) 2: Tl(O(x),y) -> Wr(x,check(y)) 3: Tl(N(x),y) -> Wr(check(x),y) 4: Tl(N(x),y) -> Wr(x,check(y)) 5: Tr(x,O(y)) -> Wl(check(x),y) 6: Tr(x,O(y)) -> Wl(x,check(y)) 7: Tr(x,N(y)) -> Wl(check(x),y) 8: Tr(x,N(y)) -> Wl(x,check(y)) 9: Tl(B(),y) -> Wr(check(B()),y) 10: Tl(B(),y) -> Wr(B(),check(y)) 11: Tr(x,B()) -> Wl(check(x),B()) 12: Tr(x,B()) -> Wl(x,check(B())) e1: Tl(O(x),y) ->= Wl(check(x),y) [relative] e2: Tl(O(x),y) ->= Wl(x,check(y)) [relative] e3: Tl(N(x),y) ->= Wl(check(x),y) [relative] e4: Tl(N(x),y) ->= Wl(x,check(y)) [relative] e5: Tr(x,O(y)) ->= Wr(check(x),y) [relative] e6: Tr(x,O(y)) ->= Wr(x,check(y)) [relative] e7: Tr(x,N(y)) ->= Wr(check(x),y) [relative] e8: Tr(x,N(y)) ->= Wr(x,check(y)) [relative] e9: B() ->= N(B()) [relative] e10: check(O(x)) ->= ok(O(x)) [relative] e11: Wl(ok(x),y) ->= Tl(x,y) [relative] e12: Wl(x,ok(y)) ->= Tl(x,y) [relative] e13: Wr(ok(x),y) ->= Tr(x,y) [relative] e14: Wr(x,ok(y)) ->= Tr(x,y) [relative] e15: check(O(x)) ->= O(check(x)) [relative] e16: check(N(x)) ->= N(check(x)) [relative] e17: O(ok(x)) ->= ok(O(x)) [relative] e18: N(ok(x)) ->= ok(N(x)) [relative] Dependency Pairs: #1: # Tl(O(x),y) -> # Wr(x,check(y)) #2: # Tr(x,O(y)) -> # Wl(x,check(y)) #3: # Wr(x,ok(y)) -> # Tr(x,y) [relative] #4: # Tl(B(),y) -> # Wr(check(B()),y) #5: # Tr(x,B()) -> # Wl(check(x),B()) #6: # Tl(N(x),y) -> # Wl(check(x),y) [relative] #7: # Tl(O(x),y) -> # Wl(x,check(y)) [relative] #8: # Tr(x,B()) -> # Wl(x,check(B())) #9: # Tr(x,N(y)) -> # Wr(x,check(y)) [relative] #10: # Wl(ok(x),y) -> # Tl(x,y) [relative] #11: # Tr(x,N(y)) -> # Wl(check(x),y) #12: # Tl(B(),y) -> # Wr(B(),check(y)) #13: # Tr(x,O(y)) -> # Wl(check(x),y) #14: # Tr(x,O(y)) -> # Wr(x,check(y)) [relative] #15: # Wl(x,ok(y)) -> # Tl(x,y) [relative] #16: # Tl(N(x),y) -> # Wl(x,check(y)) [relative] #17: # Tl(O(x),y) -> # Wl(check(x),y) [relative] #18: # Wr(ok(x),y) -> # Tr(x,y) [relative] #19: # Tl(N(x),y) -> # Wr(check(x),y) #20: # Tl(O(x),y) -> # Wr(check(x),y) #21: # Tr(x,N(y)) -> # Wl(x,check(y)) #22: # Tr(x,N(y)) -> # Wr(check(x),y) [relative] #23: # Tl(N(x),y) -> # Wr(x,check(y)) #24: # Tr(x,O(y)) -> # Wr(check(x),y) [relative] Number of SCCs: 1 SCC { #1..24 } POLO(Sum)... removes: #1 #7 #17 #20 I(# Wl) = max(x1 + 1, 0) I(# Tr) = max(x1 + 1, 0) I(Tl) = max(x1 - 1, 0) I(O) = max(x1 + 1, 0) I(B) = 1 I(check) = max(x1, 0) I(# Tl) = max(x1 + 1, 0) I(ok) = max(x1, 0) I(Tr) = max(x1 - 1, 0) I(Wr) = max(x1 - 1, 0) I(# Wr) = max(x1 + 1, 0) I(N) = max(x1, 0) I(Wl) = max(x1 - 1, 0) Number of SCCs: 1 SCC { #2..6 #8..16 #18 #19 #21..24 } POLO(Sum)... removes: #4 I(# Wl) = max(x1 - 2, 0) I(# Tr) = max(x1 - 2, 0) I(Tl) = 0 I(O) = 0 I(B) = 3 I(check) = 1 I(# Tl) = max(x1 - 2, 0) I(ok) = max(x1, 0) I(Tr) = 0 I(Wr) = 0 I(# Wr) = max(x1 - 2, 0) I(N) = max(x1, 0) I(Wl) = 0 Number of SCCs: 1 SCC { #2 #3 #5 #6 #8..16 #18 #19 #21..24 } POLO(Sum)... removes: #2 #13 #14 #24 I(# Wl) = max(x2 + 1, 0) I(# Tr) = max(x2 + 1, 0) I(Tl) = 0 I(O) = max(x1 + 1, 0) I(B) = 3 I(check) = max(x1, 0) I(# Tl) = max(x2 + 1, 0) I(ok) = max(x1, 0) I(Tr) = 0 I(Wr) = 0 I(# Wr) = max(x2 + 1, 0) I(N) = max(x1, 0) I(Wl) = 0 Number of SCCs: 1 SCC { #3 #5 #6 #8..12 #15 #16 #18 #19 #21..23 } POLO(Sum)... removes: #8 I(# Wl) = max(x2 - 2, 0) I(# Tr) = max(x2 - 2, 0) I(Tl) = 0 I(O) = 0 I(B) = 3 I(check) = 1 I(# Tl) = max(x2 - 2, 0) I(ok) = max(x1, 0) I(Tr) = 0 I(Wr) = 0 I(# Wr) = max(x2 - 2, 0) I(N) = max(x1, 0) I(Wl) = 0 Number of SCCs: 1 SCC { #3 #5 #6 #9..12 #15 #16 #18 #19 #21..23 } POLO(Sum)... QLPOS... QWPOpS(mSum)... Mat2b... failed.