YES Input TRS: 1: r1(a(x1)) -> a(a(a(r1(x1)))) 2: r2(a(x1)) -> a(a(a(r2(x1)))) 3: a(l1(x1)) -> l1(a(a(a(x1)))) 4: a(a(l2(x1))) -> l2(a(a(x1))) 5: r1(b(x1)) -> l1(b(x1)) 6: r2(b(x1)) -> l2(a(b(x1))) 7: b(l1(x1)) -> b(r2(x1)) 8: b(l2(x1)) -> b(r1(x1)) 9: a(a(x1)) -> x1 Number of strict rules: 9 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #r2(a(x1)) -> #a(a(a(r2(x1)))) #2: #r2(a(x1)) -> #a(a(r2(x1))) #3: #r2(a(x1)) -> #a(r2(x1)) #4: #r2(a(x1)) -> #r2(x1) #5: #r2(b(x1)) -> #a(b(x1)) #6: #b(l1(x1)) -> #b(r2(x1)) #7: #b(l1(x1)) -> #r2(x1) #8: #a(l1(x1)) -> #a(a(a(x1))) #9: #a(l1(x1)) -> #a(a(x1)) #10: #a(l1(x1)) -> #a(x1) #11: #r1(a(x1)) -> #a(a(a(r1(x1)))) #12: #r1(a(x1)) -> #a(a(r1(x1))) #13: #r1(a(x1)) -> #a(r1(x1)) #14: #r1(a(x1)) -> #r1(x1) #15: #b(l2(x1)) -> #b(r1(x1)) #16: #b(l2(x1)) -> #r1(x1) #17: #a(a(l2(x1))) -> #a(a(x1)) #18: #a(a(l2(x1))) -> #a(x1) Number of SCCs: 4, DPs: 9 SCC { #14 } POLO(Sum)... succeeded. a w: x1 + 1 b w: 0 l1 w: 0 l2 w: 0 #r1 w: x1 r1 w: 0 #r2 w: 0 #a w: 0 r2 w: 0 #b w: 0 USABLE RULES: { } Removed DPs: #14 Number of SCCs: 3, DPs: 8 SCC { #4 } POLO(Sum)... succeeded. a w: x1 + 1 b w: 0 l1 w: 0 l2 w: 0 #r1 w: 0 r1 w: 0 #r2 w: x1 #a w: 0 r2 w: 0 #b w: 0 USABLE RULES: { } Removed DPs: #4 Number of SCCs: 2, DPs: 7 SCC { #6 #15 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. a w: [0,1;1,0] * x1 b w: [0;2] l1 w: x1 + [39090;39090] l2 w: [0,0;0,1] * x1 + [8557;39091] #r1 w: [0;0] r1 w: x1 + [39090;39090] #r2 w: [0;0] #a w: [0;0] r2 w: x1 + [39089;39089] #b w: [0,1;0,0] * x1 USABLE RULES: { 1..9 } Removed DPs: #6 #15 Number of SCCs: 1, DPs: 5 SCC { #8..10 #17 #18 } POLO(Sum)... succeeded. a w: x1 b w: 20977 l1 w: x1 + 15922 l2 w: x1 + 8946 #r1 w: 0 r1 w: 14681 #r2 w: 0 #a w: x1 r2 w: 2998 #b w: 0 USABLE RULES: { 3 4 7..9 } Removed DPs: #8..10 #17 #18 Number of SCCs: 0, DPs: 0