YES Input TRS: 1: f(b(a(),z)) -> z 2: b(y,b(a(),z)) -> b(f(c(y,y,a())),b(f(z),a())) 3: f(f(f(c(z,x,a())))) -> b(f(x),z) Number of strict rules: 3 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #b(y,b(a(),z)) -> #b(f(c(y,y,a())),b(f(z),a())) #2: #b(y,b(a(),z)) -> #f(c(y,y,a())) #3: #b(y,b(a(),z)) -> #b(f(z),a()) #4: #b(y,b(a(),z)) -> #f(z) #5: #f(f(f(c(z,x,a())))) -> #b(f(x),z) #6: #f(f(f(c(z,x,a())))) -> #f(x) Number of SCCs: 1, DPs: 4 SCC { #1 #4..6 } POLO(Sum)... succeeded. a w: 0 b w: x2 + 8370 c w: x1 + x2 + x3 + 1 f w: x1 + 1 #f w: x1 + 8369 #b w: x2 USABLE RULES: { } Removed DPs: #4..6 Number of SCCs: 1, DPs: 1 SCC { #1 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. a w: [1;0] b w: [1,0;1,0] * x1 + [0,1;1,1] * x2 + [2655;0] c w: [0,1;1,0] * x1 + [1,1;0,0] * x2 + [24128;0] f w: [0,1;1,1] * x1 + [0;1] #f w: [0;0] #b w: x2 USABLE RULES: { 1..3 } Removed DPs: #1 Number of SCCs: 0, DPs: 0