YES Input TRS: 1: 0(1(2(3(4(5(1(x1))))))) -> 0(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))) 2: 0(1(2(3(4(5(1(x1))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))))))))) 3: 0(1(2(3(4(5(1(x1))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))))))))))))))) Number of strict rules: 3 Direct POLO(bPol) ... failed. Uncurrying 0^1_1^1_2 0^1_1 0 1: 0^1_1^1_2^1_3(4(5(1(x1)))) -> 0^1_2(3(4(5(1(1(0^1_1^1_2^1_3(4(5(0^1_1^1_2^1_3(4(5(x1)))))))))))) 2: 0^1_1^1_2^1_3(4(5(1(x1)))) -> 1(2(3(4(5(1(1(0^1_1^1_2^1_3(4(5(0^1_1^1_2^1_3(4(5(0^1_1^1_2^1_3(4(5(x1)))))))))))))))) 3: 0^1_1^1_2^1_3(4(5(1(x1)))) -> 1(2(3(4(5(1(1(0^1_1^1_2^1_3(4(5(0^1_1^1_2^1_3(4(5(0^1_1^1_2^1_3(4(5(0^1_1^1_2^1_3(4(5(x1))))))))))))))))))) 4: 0(2(_1)) ->= 0^1_2(_1) 5: 0(1(_1)) ->= 0^1_1(_1) 6: 0^1_1(2(_1)) ->= 0^1_1^1_2(_1) 7: 0^1_1^1_2(3(_1)) ->= 0^1_1^1_2^1_3(_1) Number of strict rules: 3 Direct POLO(bPol) ... removes: 4 5 7 6 1 w: x1 4 w: x1 5 w: x1 3 w: x1 0^1_1^1_2 w: x1 + 1 0 w: x1 + 3451 0^1_1 w: x1 + 2 2 w: x1 0^1_1^1_2^1_3 w: x1 0^1_2 w: x1 Number of strict rules: 3 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #0^1_1^1_2^1_3(4(5(1(x1)))) -> #0^1_1^1_2^1_3(4(5(0^1_1^1_2^1_3(4(5(0^1_1^1_2^1_3(4(5(x1))))))))) #2: #0^1_1^1_2^1_3(4(5(1(x1)))) -> #0^1_1^1_2^1_3(4(5(0^1_1^1_2^1_3(4(5(x1)))))) #3: #0^1_1^1_2^1_3(4(5(1(x1)))) -> #0^1_1^1_2^1_3(4(5(x1))) #4: #0^1_1^1_2^1_3(4(5(1(x1)))) -> #0^1_1^1_2^1_3(4(5(0^1_1^1_2^1_3(4(5(0^1_1^1_2^1_3(4(5(0^1_1^1_2^1_3(4(5(x1)))))))))))) #5: #0^1_1^1_2^1_3(4(5(1(x1)))) -> #0^1_1^1_2^1_3(4(5(0^1_1^1_2^1_3(4(5(0^1_1^1_2^1_3(4(5(x1))))))))) #6: #0^1_1^1_2^1_3(4(5(1(x1)))) -> #0^1_1^1_2^1_3(4(5(0^1_1^1_2^1_3(4(5(x1)))))) #7: #0^1_1^1_2^1_3(4(5(1(x1)))) -> #0^1_1^1_2^1_3(4(5(x1))) #8: #0^1_1^1_2^1_3(4(5(1(x1)))) -> #0^1_1^1_2^1_3(4(5(0^1_1^1_2^1_3(4(5(x1)))))) #9: #0^1_1^1_2^1_3(4(5(1(x1)))) -> #0^1_1^1_2^1_3(4(5(x1))) Number of SCCs: 1, DPs: 9 SCC { #1..9 } POLO(Sum)... succeeded. 1 w: x1 + 4 4 w: x1 5 w: x1 + 1 3 w: x1 0^1_1^1_2 w: 0 0 w: 0 #0^1_1^1_2^1_3 w: x1 0^1_1 w: 0 2 w: 1 0^1_1^1_2^1_3 w: x1 0^1_2 w: 5 USABLE RULES: { 1..3 } Removed DPs: #1..9 Number of SCCs: 0, DPs: 0