YES Input TRS: 1: 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(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))))))))))))))))))))))))) Number of strict rules: 2 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)))) -> 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)) ->= 0^1_1(_1) 4: 0^1_1(2(_1)) ->= 0^1_1^1_2(_1) 5: 0^1_1^1_2(3(_1)) ->= 0^1_1^1_2^1_3(_1) Number of strict rules: 2 Direct POLO(bPol) ... removes: 4 3 5 1 w: x1 4 w: x1 5 w: x1 3 w: x1 0^1_1^1_2 w: x1 + 2 0 w: 2 * x1 + 4 0^1_1 w: 2 * x1 + 3 2 w: x1 0^1_1^1_2^1_3 w: x1 Number of strict rules: 2 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(x1)))))) #5: #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: 5 SCC { #1..5 } POLO(Sum)... succeeded. 1 w: x1 + 22587 4 w: x1 + 11292 5 w: x1 + 1 3 w: 1 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: 8366 0^1_1^1_2^1_3 w: x1 USABLE RULES: { 1 2 } Removed DPs: #1..5 Number of SCCs: 0, DPs: 0