YES Input TRS: 1: 0(1(2(x1))) -> 0(1(3(2(x1)))) 2: 0(1(2(x1))) -> 0(2(1(0(x1)))) 3: 0(1(2(x1))) -> 0(2(1(3(x1)))) 4: 0(1(2(x1))) -> 0(2(2(1(x1)))) 5: 0(1(2(x1))) -> 0(2(2(1(4(x1))))) 6: 0(1(2(x1))) -> 5(1(0(5(2(3(x1)))))) 7: 0(2(4(x1))) -> 0(2(1(4(3(x1))))) 8: 0(4(2(x1))) -> 4(0(2(3(x1)))) 9: 0(4(2(x1))) -> 4(0(5(5(2(x1))))) 10: 0(0(4(2(x1)))) -> 0(0(2(2(3(4(x1)))))) 11: 0(1(2(2(x1)))) -> 0(2(1(0(2(x1))))) 12: 0(1(2(2(x1)))) -> 1(3(0(2(2(x1))))) 13: 0(1(2(4(x1)))) -> 0(1(4(2(3(x1))))) 14: 0(1(2(4(x1)))) -> 4(0(2(2(1(1(x1)))))) 15: 0(1(2(4(x1)))) -> 4(0(5(5(2(1(x1)))))) 16: 0(1(2(5(x1)))) -> 3(5(5(2(1(0(x1)))))) 17: 0(1(4(2(x1)))) -> 0(5(2(1(4(x1))))) 18: 0(1(5(2(x1)))) -> 1(5(0(2(3(x1))))) 19: 0(1(5(2(x1)))) -> 0(2(2(1(0(5(x1)))))) 20: 0(1(5(2(x1)))) -> 5(5(0(2(1(3(x1)))))) 21: 0(2(4(2(x1)))) -> 0(5(4(3(2(2(x1)))))) 22: 0(3(1(2(x1)))) -> 0(2(1(3(2(x1))))) 23: 0(3(1(2(x1)))) -> 1(0(2(5(3(x1))))) 24: 0(3(1(2(x1)))) -> 1(5(0(2(3(x1))))) 25: 0(3(1(2(x1)))) -> 3(0(2(2(1(x1))))) 26: 0(3(1(2(x1)))) -> 3(2(2(1(0(x1))))) 27: 0(3(1(2(x1)))) -> 0(3(2(3(1(3(x1)))))) 28: 0(3(4(2(x1)))) -> 0(2(2(3(4(x1))))) 29: 5(0(1(2(x1)))) -> 1(3(2(5(0(x1))))) 30: 5(0(1(2(x1)))) -> 5(0(2(1(3(3(x1)))))) 31: 0(1(1(2(5(x1))))) -> 5(0(2(5(1(1(x1)))))) 32: 0(2(3(4(2(x1))))) -> 3(2(2(3(4(0(x1)))))) 33: 0(3(1(2(5(x1))))) -> 2(3(1(3(0(5(x1)))))) 34: 0(3(1(5(2(x1))))) -> 0(3(2(5(1(2(x1)))))) 35: 0(3(4(1(4(x1))))) -> 0(5(3(1(4(4(x1)))))) 36: 0(3(5(1(2(x1))))) -> 5(5(3(2(1(0(x1)))))) 37: 0(4(0(4(2(x1))))) -> 4(4(0(0(2(2(x1)))))) 38: 0(4(1(1(2(x1))))) -> 3(1(4(0(2(1(x1)))))) 39: 0(4(1(2(2(x1))))) -> 4(1(0(2(2(3(x1)))))) 40: 0(4(1(2(5(x1))))) -> 3(4(1(0(2(5(x1)))))) 41: 0(4(2(1(2(x1))))) -> 4(1(3(2(0(2(x1)))))) 42: 0(4(2(1(4(x1))))) -> 0(2(1(4(4(4(x1)))))) 43: 0(4(2(5(2(x1))))) -> 5(4(3(2(2(0(x1)))))) 44: 0(4(5(1(2(x1))))) -> 1(4(2(0(5(5(x1)))))) 45: 0(4(5(1(2(x1))))) -> 4(0(2(5(1(1(x1)))))) 46: 5(0(1(2(2(x1))))) -> 5(0(2(2(1(2(x1)))))) 47: 5(0(2(4(2(x1))))) -> 0(2(2(5(1(4(x1)))))) 48: 5(0(4(4(2(x1))))) -> 0(5(2(5(4(4(x1)))))) Number of strict rules: 48 Direct POLO(bPol) ... failed. Uncurrying 0^1_2 0 1: 0^1_1(2(x1)) -> 0^1_1(3(2(x1))) 2: 0^1_1(2(x1)) -> 0^1_2^1_1(0(x1)) 3: 0^1_1(2(x1)) -> 0^1_2^1_1(3(x1)) 4: 0^1_1(2(x1)) -> 0^1_2^1_2(1(x1)) 5: 0^1_1(2(x1)) -> 0^1_2^1_2(1(4(x1))) 6: 0^1_1(2(x1)) -> 5(1(0(5(2(3(x1)))))) 7: 0^1_2^1_4(x1) -> 0^1_2^1_1(4(3(x1))) 8: 0^1_4(2(x1)) -> 4(0^1_2^1_3(x1)) 9: 0^1_4(2(x1)) -> 4(0(5(5(2(x1))))) 10: 0(0^1_4(2(x1))) -> 0(0^1_2^1_2(3(4(x1)))) 11: 0^1_1(2(2(x1))) -> 0^1_2^1_1(0^1_2(x1)) 12: 0^1_1(2(2(x1))) -> 1(3(0^1_2^1_2(x1))) 13: 0^1_1(2(4(x1))) -> 0^1_1(4(2(3(x1)))) 14: 0^1_1(2(4(x1))) -> 4(0^1_2^1_2(1(1(x1)))) 15: 0^1_1(2(4(x1))) -> 4(0(5(5(2(1(x1)))))) 16: 0^1_1(2(5(x1))) -> 3(5(5(2(1(0(x1)))))) 17: 0^1_1(4(2(x1))) -> 0(5(2(1(4(x1))))) 18: 0^1_1(5(2(x1))) -> 1(5(0^1_2^1_3(x1))) 19: 0^1_1(5(2(x1))) -> 0^1_2^1_2(1(0(5(x1)))) 20: 0^1_1(5(2(x1))) -> 5(5(0^1_2^1_1(3(x1)))) 21: 0^1_2^1_4(2(x1)) -> 0(5(4(3(2(2(x1)))))) 22: 0^1_3(1(2(x1))) -> 0^1_2^1_1(3(2(x1))) 23: 0^1_3(1(2(x1))) -> 1(0^1_2(5(3(x1)))) 24: 0^1_3(1(2(x1))) -> 1(5(0^1_2^1_3(x1))) 25: 0^1_3(1(2(x1))) -> 3(0^1_2^1_2(1(x1))) 26: 0^1_3(1(2(x1))) -> 3(2(2(1(0(x1))))) 27: 0^1_3(1(2(x1))) -> 0^1_3(2(3(1(3(x1))))) 28: 0^1_3(4(2(x1))) -> 0^1_2^1_2(3(4(x1))) 29: 5(0^1_1(2(x1))) -> 1(3(2(5(0(x1))))) 30: 5(0^1_1(2(x1))) -> 5(0^1_2^1_1(3(3(x1)))) 31: 0^1_1(1(2(5(x1)))) -> 5(0^1_2(5(1(1(x1))))) 32: 0^1_2^1_3(4(2(x1))) -> 3(2(2(3(4(0(x1)))))) 33: 0^1_3(1(2(5(x1)))) -> 2(3(1(3(0(5(x1)))))) 34: 0^1_3(1(5(2(x1)))) -> 0^1_3(2(5(1(2(x1))))) 35: 0^1_3(4(1(4(x1)))) -> 0(5(3(1(4(4(x1)))))) 36: 0^1_3(5(1(2(x1)))) -> 5(5(3(2(1(0(x1)))))) 37: 0^1_4(0^1_4(2(x1))) -> 4(4(0(0^1_2^1_2(x1)))) 38: 0^1_4(1(1(2(x1)))) -> 3(1(4(0^1_2^1_1(x1)))) 39: 0^1_4(1(2(2(x1)))) -> 4(1(0^1_2^1_2(3(x1)))) 40: 0^1_4(1(2(5(x1)))) -> 3(4(1(0^1_2(5(x1))))) 41: 0^1_4(2(1(2(x1)))) -> 4(1(3(2(0^1_2(x1))))) 42: 0^1_4(2(1(4(x1)))) -> 0^1_2^1_1(4(4(4(x1)))) 43: 0^1_4(2(5(2(x1)))) -> 5(4(3(2(2(0(x1)))))) 44: 0^1_4(5(1(2(x1)))) -> 1(4(2(0(5(5(x1)))))) 45: 0^1_4(5(1(2(x1)))) -> 4(0^1_2(5(1(1(x1))))) 46: 5(0^1_1(2(2(x1)))) -> 5(0^1_2^1_2(1(2(x1)))) 47: 5(0^1_2^1_4(2(x1))) -> 0^1_2^1_2(5(1(4(x1)))) 48: 5(0^1_4(4(2(x1)))) -> 0(5(2(5(4(4(x1)))))) 49: 0(2(_1)) ->= 0^1_2(_1) 50: 0(1(_1)) ->= 0^1_1(_1) 51: 0(4(_1)) ->= 0^1_4(_1) 52: 0(3(_1)) ->= 0^1_3(_1) 53: 0^1_2(2(_1)) ->= 0^1_2^1_2(_1) 54: 0^1_2(1(_1)) ->= 0^1_2^1_1(_1) 55: 0^1_2(4(_1)) ->= 0^1_2^1_4(_1) 56: 0^1_2(3(_1)) ->= 0^1_2^1_3(_1) Number of strict rules: 48 Direct POLO(bPol) ... removes: 4 54 3 22 28 5 10 39 7 20 25 30 14 12 38 53 47 37 42 46 1 w: x1 4 w: x1 + 1 5 w: x1 3 w: x1 0^1_2^1_1 w: x1 0^1_4 w: x1 + 14991 0^1_3 w: x1 + 14990 0^1_2^1_4 w: x1 + 14991 0 w: x1 + 14990 0^1_2^1_2 w: x1 0^1_2^1_3 w: x1 + 14990 0^1_1 w: x1 + 14990 2 w: x1 0^1_2 w: x1 + 14990 Number of strict rules: 30 Direct POLO(bPol) ... removes: 18 15 8 32 44 56 45 24 9 40 41 43 1 w: x1 4 w: x1 + 29044 5 w: x1 3 w: x1 0^1_2^1_1 w: x1 0^1_4 w: 2 * x1 + 87132 0^1_3 w: 2 * x1 + 29044 0^1_2^1_4 w: 2 * x1 + 87132 0 w: 2 * x1 + 29044 0^1_2^1_2 w: x1 0^1_2^1_3 w: 2 * x1 + 29043 0^1_1 w: 2 * x1 + 29044 2 w: x1 0^1_2 w: 2 * x1 + 29044 Number of strict rules: 19 Direct POLO(bPol) ... removes: 16 36 26 19 33 23 11 6 29 2 1 w: x1 + 45539 4 w: x1 + 91078 5 w: x1 3 w: x1 0^1_2^1_1 w: x1 + 28216 0^1_4 w: 2 * x1 + 253844 0^1_3 w: 2 * x1 + 71688 0^1_2^1_4 w: 2 * x1 + 253844 0 w: 2 * x1 + 71688 0^1_2^1_2 w: x1 + 26149 0^1_2^1_3 w: 2 * x1 + 71688 0^1_1 w: 2 * x1 + 162766 2 w: x1 0^1_2 w: 2 * x1 + 71688 Number of strict rules: 9 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #0^1_3(4(1(4(x1)))) -> #0(5(3(1(4(4(x1)))))) #2: #0^1_3(4(1(4(x1)))) -> #5(3(1(4(4(x1))))) #3: #5(0^1_4(4(2(x1)))) -> #0(5(2(5(4(4(x1)))))) #4: #5(0^1_4(4(2(x1)))) -> #5(2(5(4(4(x1))))) #5: #5(0^1_4(4(2(x1)))) -> #5(4(4(x1))) #6: #0^1_2(4(_1)) ->? #0^1_2^1_4(_1) #7: #0^1_1(2(4(x1))) -> #0^1_1(4(2(3(x1)))) #8: #0^1_1(1(2(5(x1)))) -> #5(0^1_2(5(1(1(x1))))) #9: #0^1_1(1(2(5(x1)))) -> #0^1_2(5(1(1(x1)))) #10: #0^1_1(1(2(5(x1)))) -> #5(1(1(x1))) #11: #0(3(_1)) ->? #0^1_3(_1) #12: #0(2(_1)) ->? #0^1_2(_1) #13: #0^1_3(1(5(2(x1)))) -> #0^1_3(2(5(1(2(x1))))) #14: #0^1_3(1(5(2(x1)))) -> #5(1(2(x1))) #15: #0^1_3(1(2(x1))) -> #0^1_3(2(3(1(3(x1))))) #16: #0^1_1(4(2(x1))) -> #0(5(2(1(4(x1))))) #17: #0^1_1(4(2(x1))) -> #5(2(1(4(x1)))) #18: #0^1_2^1_4(2(x1)) -> #0(5(4(3(2(2(x1)))))) #19: #0^1_2^1_4(2(x1)) -> #5(4(3(2(2(x1))))) #20: #0^1_1(2(x1)) -> #0^1_1(3(2(x1))) #21: #0(1(_1)) ->? #0^1_1(_1) Number of SCCs: 0, DPs: 0