YES Input TRS: 1: b(a(),b(c(z,x,y),a())) -> b(b(z,c(y,z,a())),x) 2: f(c(a(),b(b(z,a()),y),x)) -> f(c(x,b(z,x),y)) 3: c(f(c(a(),y,a())),x,z) -> f(b(b(z,z),f(b(y,b(x,a()))))) Number of strict rules: 3 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #f(c(a(),b(b(z,a()),y),x)) -> #f(c(x,b(z,x),y)) #2: #f(c(a(),b(b(z,a()),y),x)) -> #c(x,b(z,x),y) #3: #f(c(a(),b(b(z,a()),y),x)) -> #b(z,x) #4: #c(f(c(a(),y,a())),x,z) -> #f(b(b(z,z),f(b(y,b(x,a()))))) #5: #c(f(c(a(),y,a())),x,z) -> #b(b(z,z),f(b(y,b(x,a())))) #6: #c(f(c(a(),y,a())),x,z) -> #b(z,z) #7: #c(f(c(a(),y,a())),x,z) -> #f(b(y,b(x,a()))) #8: #c(f(c(a(),y,a())),x,z) -> #b(y,b(x,a())) #9: #c(f(c(a(),y,a())),x,z) -> #b(x,a()) #10: #b(a(),b(c(z,x,y),a())) -> #b(b(z,c(y,z,a())),x) #11: #b(a(),b(c(z,x,y),a())) -> #b(z,c(y,z,a())) #12: #b(a(),b(c(z,x,y),a())) -> #c(y,z,a()) Number of SCCs: 2, DPs: 4 SCC { #1 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. a w: [1;1] b w: [1,0;1,0] * x1 + [0,1;0,1] * x2 + [1;1] c w: [1,1;0,0] * x1 + [0,1;0,1] * x2 + x3 + [48539;44179] f w: [25150;32066] #f w: [0,1;0,0] * x1 #c w: [0;0] #b w: [0;0] USABLE RULES: { 1 3 } Removed DPs: #1 Number of SCCs: 1, DPs: 3 SCC { #6 #8 #12 } POLO(Sum)... succeeded. a w: 0 b w: x2 + 10795 c w: x2 + 40328 f w: x1 + 3972 #f w: 0 #c w: x3 + 10795 #b w: x2 USABLE RULES: { } Removed DPs: #6 Number of SCCs: 1, DPs: 2 SCC { #8 #12 } POLO(Sum)... succeeded. a w: 9945 b w: x1 + x2 + 25252 c w: x1 + x2 + x3 + 8617 f w: x1 #f w: 0 #c w: x1 + x2 + x3 + 33868 #b w: x2 USABLE RULES: { } Removed DPs: #8 #12 Number of SCCs: 0, DPs: 0