0.00/0.03 YES 0.00/0.04 Input TRS: 0.00/0.04 C symbols: eq 0.00/0.04 1: eq(0(),0()) -> true() 0.00/0.04 2: eq(0(),s(x)) -> false() 0.00/0.04 3: eq(s(x),0()) -> false() 0.00/0.04 4: eq(s(x),s(y)) -> eq(x,y) 0.00/0.04 5: rm(n,nil()) -> nil() 0.00/0.04 6: rm(n,add(m,x)) -> if_rm(eq(n,m),n,add(m,x)) 0.00/0.04 7: if_rm(true(),n,add(m,x)) -> rm(n,x) 0.00/0.04 8: if_rm(false(),n,add(m,x)) -> add(m,rm(n,x)) 0.00/0.04 9: purge(nil()) -> nil() 0.00/0.04 10: purge(add(n,x)) -> add(n,purge(rm(n,x))) 0.00/0.04 Number of strict rules: 10 0.00/0.04 Direct POLO(bPol) ... failed. 0.00/0.04 Uncurrying ... failed. 0.00/0.04 Dependency Pairs: 0.00/0.04 #1: #rm(n,add(m,x)) -> #if_rm(eq(n,m),n,add(m,x)) 0.00/0.04 #2: #rm(n,add(m,x)) -> #eq(n,m) 0.00/0.04 #3: #if_rm(true(),n,add(m,x)) -> #rm(n,x) 0.00/0.04 #4: #purge(add(n,x)) -> #purge(rm(n,x)) 0.00/0.04 #5: #purge(add(n,x)) -> #rm(n,x) 0.00/0.04 #6: #if_rm(false(),n,add(m,x)) -> #rm(n,x) 0.00/0.04 #7: #eq(s(x),s(y)) -> #eq(x,y) 0.00/0.04 Number of SCCs: 3, DPs: 5 0.00/0.04 SCC { #4 } 0.00/0.04 POLO(Sum)... succeeded. 0.00/0.04 if_rm w: x1 + x2 + x3 0.00/0.04 s w: 1 0.00/0.04 #if_rm w: 0 0.00/0.04 #purge w: x1 0.00/0.04 eq w: 1 0.00/0.04 false w: 1 0.00/0.04 true w: 1 0.00/0.04 purge w: 0 0.00/0.04 #eq w: 0 0.00/0.04 0 w: 1 0.00/0.04 nil w: 1 0.00/0.04 add w: x1 + x2 + 2 0.00/0.04 rm w: x1 + x2 + 1 0.00/0.04 #rm w: 0 0.00/0.04 USABLE RULES: { 1..8 } 0.00/0.04 Removed DPs: #4 0.00/0.04 Number of SCCs: 2, DPs: 4 0.00/0.04 SCC { #7 } 0.00/0.04 POLO(Sum)... succeeded. 0.00/0.04 if_rm w: x1 + x2 + x3 0.00/0.04 s w: x1 + 1 0.00/0.04 #if_rm w: 0 0.00/0.04 #purge w: x1 0.00/0.04 eq w: 1 0.00/0.04 false w: 1 0.00/0.04 true w: 1 0.00/0.04 purge w: 0 0.00/0.04 #eq w: x1 + x2 0.00/0.04 0 w: 1 0.00/0.04 nil w: 1 0.00/0.04 add w: x1 + x2 + 2 0.00/0.04 rm w: x1 + x2 + 1 0.00/0.04 #rm w: 0 0.00/0.04 USABLE RULES: { 1..8 } 0.00/0.04 Removed DPs: #7 0.00/0.04 Number of SCCs: 1, DPs: 3 0.00/0.04 SCC { #1 #3 #6 } 0.00/0.04 POLO(Sum)... succeeded. 0.00/0.04 if_rm w: x1 + x2 + x3 0.00/0.04 s w: x1 + 1 0.00/0.04 #if_rm w: x1 + x2 + x3 0.00/0.04 #purge w: x1 0.00/0.04 eq w: 1 0.00/0.04 false w: 1 0.00/0.04 true w: 1 0.00/0.04 purge w: 0 0.00/0.04 #eq w: 0 0.00/0.04 0 w: 1 0.00/0.04 nil w: 1 0.00/0.04 add w: x2 + 2 0.00/0.04 rm w: x1 + x2 + 1 0.00/0.04 #rm w: x1 + x2 + 2 0.00/0.04 USABLE RULES: { 1..8 } 0.00/0.04 Removed DPs: #1 #3 #6 0.00/0.04 Number of SCCs: 0, DPs: 0 0.00/0.04 Next Dependency Pairs: 0.00/0.04 Number of SCCs: 0, DPs: 0 0.00/0.04 EOF