YES Input TRS: 1: a(a(b(b(x1)))) -> b(b(c(c(a(a(x1)))))) 2: b(b(c(c(x1)))) -> c(c(b(b(b(b(x1)))))) 3: b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) Number of strict rules: 3 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #b(b(c(c(x1)))) -> #b(b(b(b(x1)))) #2: #b(b(c(c(x1)))) -> #b(b(b(x1))) #3: #b(b(c(c(x1)))) -> #b(b(x1)) #4: #b(b(c(c(x1)))) -> #b(x1) #5: #b(b(a(a(x1)))) -> #a(a(c(c(b(b(x1)))))) #6: #b(b(a(a(x1)))) -> #a(c(c(b(b(x1))))) #7: #b(b(a(a(x1)))) -> #b(b(x1)) #8: #b(b(a(a(x1)))) -> #b(x1) #9: #a(a(b(b(x1)))) -> #b(b(c(c(a(a(x1)))))) #10: #a(a(b(b(x1)))) -> #b(c(c(a(a(x1))))) #11: #a(a(b(b(x1)))) -> #a(a(x1)) #12: #a(a(b(b(x1)))) -> #a(x1) Number of SCCs: 2, DPs: 8 SCC { #11 #12 } POLO(Sum)... succeeded. a w: x1 + 1 b w: x1 + 30094 c w: 2 #a w: x1 #b w: 0 USABLE RULES: { 1..3 } Removed DPs: #11 #12 Number of SCCs: 1, DPs: 6 SCC { #1..4 #7 #8 } POLO(Sum)... succeeded. a w: x1 + 10451 b w: x1 c w: x1 #a w: x1 #b w: x1 USABLE RULES: { 1..3 } Removed DPs: #7 #8 Number of SCCs: 1, DPs: 4 SCC { #1..4 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. a w: [1,0;1,0] * x1 + [21245;1] b w: x1 + [1;0] c w: [0,0;0,1] * x1 + [0;1] #a w: [0;0] #b w: [0,1;0,0] * x1 USABLE RULES: { 1..3 } Removed DPs: #1..4 Number of SCCs: 0, DPs: 0