YES Input TRS: 1: times(x,0()) -> 0() 2: times(x,s(y)) -> plus(times(x,y),x) 3: plus(x,0()) -> x 4: plus(0(),x) -> x 5: plus(x,s(y)) -> s(plus(x,y)) 6: plus(s(x),y) -> s(plus(x,y)) Number of strict rules: 6 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #times(x,s(y)) -> #plus(times(x,y),x) #2: #times(x,s(y)) -> #times(x,y) #3: #plus(s(x),y) -> #plus(x,y) #4: #plus(x,s(y)) -> #plus(x,y) Number of SCCs: 2, DPs: 3 SCC { #2 } POLO(Sum)... succeeded. s w: x1 + 1 #plus w: 0 #times w: x2 0 w: 0 times w: 0 plus w: 0 USABLE RULES: { } Removed DPs: #2 Number of SCCs: 1, DPs: 2 SCC { #3 #4 } POLO(Sum)... succeeded. s w: x1 + 1 #plus w: x1 #times w: 0 0 w: 0 times w: 0 plus w: 0 USABLE RULES: { } Removed DPs: #3 Number of SCCs: 1, DPs: 1 SCC { #4 } POLO(Sum)... succeeded. s w: x1 + 1 #plus w: x2 #times w: 0 0 w: 0 times w: 0 plus w: 0 USABLE RULES: { } Removed DPs: #4 Number of SCCs: 0, DPs: 0