YES Input TRS: 1: b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z))))) 2: c(f(f(c(x,a(),z))),a(),y) -> b(y,f(b(a(),z))) 3: b(b(c(b(a(),a()),a(),z),f(a())),y) -> z Number of strict rules: 3 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #c(f(f(c(x,a(),z))),a(),y) -> #b(y,f(b(a(),z))) #2: #c(f(f(c(x,a(),z))),a(),y) -> #b(a(),z) #3: #b(f(b(x,z)),y) -> #b(z,b(y,z)) #4: #b(f(b(x,z)),y) -> #b(y,z) Number of SCCs: 1, DPs: 2 SCC { #3 #4 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. a w: [1;1] b w: [1,0;1,0] * x1 + [0,0;1,0] * x2 + [25575;17220] c w: [0,0;0,1] * x1 + [1,0;0,0] * x2 + [1,1;0,0] * x3 + [8784;0] f w: [0,1;0,0] * x1 + [8356;13020] #c w: [0;0] #b w: [1,0;0,0] * x1 + [1,0;0,0] * x2 USABLE RULES: { 1 3 } Removed DPs: #3 #4 Number of SCCs: 0, DPs: 0