1.51/1.57 YES 1.51/1.57 Input TRS: 1.51/1.57 1: 0(1(2(x1))) -> 0(1(3(2(x1)))) 1.51/1.57 2: 0(1(2(x1))) -> 0(2(1(0(x1)))) 1.51/1.57 3: 0(1(2(x1))) -> 0(2(1(3(x1)))) 1.51/1.57 4: 0(1(2(x1))) -> 0(2(2(1(x1)))) 1.51/1.57 5: 0(1(2(x1))) -> 0(2(2(1(4(x1))))) 1.51/1.57 6: 0(1(2(x1))) -> 5(1(0(5(2(3(x1)))))) 1.51/1.57 7: 0(2(4(x1))) -> 0(2(1(4(3(x1))))) 1.51/1.57 8: 0(4(2(x1))) -> 4(0(2(3(x1)))) 1.51/1.57 9: 0(4(2(x1))) -> 4(0(5(5(2(x1))))) 1.51/1.57 10: 0(0(4(2(x1)))) -> 0(0(2(2(3(4(x1)))))) 1.51/1.57 11: 0(1(2(2(x1)))) -> 0(2(1(0(2(x1))))) 1.51/1.57 12: 0(1(2(2(x1)))) -> 1(3(0(2(2(x1))))) 1.51/1.57 13: 0(1(2(4(x1)))) -> 0(1(4(2(3(x1))))) 1.51/1.57 14: 0(1(2(4(x1)))) -> 4(0(2(2(1(1(x1)))))) 1.51/1.57 15: 0(1(2(4(x1)))) -> 4(0(5(5(2(1(x1)))))) 1.51/1.57 16: 0(1(2(5(x1)))) -> 3(5(5(2(1(0(x1)))))) 1.51/1.57 17: 0(1(4(2(x1)))) -> 0(5(2(1(4(x1))))) 1.51/1.57 18: 0(1(5(2(x1)))) -> 1(5(0(2(3(x1))))) 1.51/1.57 19: 0(1(5(2(x1)))) -> 0(2(2(1(0(5(x1)))))) 1.51/1.57 20: 0(1(5(2(x1)))) -> 5(5(0(2(1(3(x1)))))) 1.51/1.57 21: 0(2(4(2(x1)))) -> 0(5(4(3(2(2(x1)))))) 1.51/1.57 22: 0(3(1(2(x1)))) -> 0(2(1(3(2(x1))))) 1.51/1.57 23: 0(3(1(2(x1)))) -> 1(0(2(5(3(x1))))) 1.51/1.57 24: 0(3(1(2(x1)))) -> 1(5(0(2(3(x1))))) 1.51/1.57 25: 0(3(1(2(x1)))) -> 3(0(2(2(1(x1))))) 1.51/1.57 26: 0(3(1(2(x1)))) -> 3(2(2(1(0(x1))))) 1.51/1.57 27: 0(3(1(2(x1)))) -> 0(3(2(3(1(3(x1)))))) 1.51/1.57 28: 0(3(4(2(x1)))) -> 0(2(2(3(4(x1))))) 1.51/1.57 29: 5(0(1(2(x1)))) -> 1(3(2(5(0(x1))))) 1.51/1.57 30: 5(0(1(2(x1)))) -> 5(0(2(1(3(3(x1)))))) 1.51/1.57 31: 0(1(1(2(5(x1))))) -> 5(0(2(5(1(1(x1)))))) 1.51/1.57 32: 0(2(3(4(2(x1))))) -> 3(2(2(3(4(0(x1)))))) 1.51/1.57 33: 0(3(1(2(5(x1))))) -> 2(3(1(3(0(5(x1)))))) 1.51/1.57 34: 0(3(1(5(2(x1))))) -> 0(3(2(5(1(2(x1)))))) 1.51/1.57 35: 0(3(4(1(4(x1))))) -> 0(5(3(1(4(4(x1)))))) 1.51/1.57 36: 0(3(5(1(2(x1))))) -> 5(5(3(2(1(0(x1)))))) 1.51/1.57 37: 0(4(0(4(2(x1))))) -> 4(4(0(0(2(2(x1)))))) 1.51/1.57 38: 0(4(1(1(2(x1))))) -> 3(1(4(0(2(1(x1)))))) 1.51/1.57 39: 0(4(1(2(2(x1))))) -> 4(1(0(2(2(3(x1)))))) 1.51/1.57 40: 0(4(1(2(5(x1))))) -> 3(4(1(0(2(5(x1)))))) 1.51/1.57 41: 0(4(2(1(2(x1))))) -> 4(1(3(2(0(2(x1)))))) 1.51/1.57 42: 0(4(2(1(4(x1))))) -> 0(2(1(4(4(4(x1)))))) 1.51/1.57 43: 0(4(2(5(2(x1))))) -> 5(4(3(2(2(0(x1)))))) 1.51/1.57 44: 0(4(5(1(2(x1))))) -> 1(4(2(0(5(5(x1)))))) 1.51/1.57 45: 0(4(5(1(2(x1))))) -> 4(0(2(5(1(1(x1)))))) 1.51/1.57 46: 5(0(1(2(2(x1))))) -> 5(0(2(2(1(2(x1)))))) 1.51/1.57 47: 5(0(2(4(2(x1))))) -> 0(2(2(5(1(4(x1)))))) 1.51/1.57 48: 5(0(4(4(2(x1))))) -> 0(5(2(5(4(4(x1)))))) 1.51/1.57 Number of strict rules: 48 1.51/1.57 Direct POLO(bPol) ... failed. 1.51/1.57 Uncurrying 0^1_2 0 1.51/1.57 1: 0^1_1(2(x1)) -> 0^1_1(3(2(x1))) 1.51/1.57 2: 0^1_1(2(x1)) -> 0^1_2^1_1(0(x1)) 1.51/1.57 3: 0^1_1(2(x1)) -> 0^1_2^1_1(3(x1)) 1.51/1.57 4: 0^1_1(2(x1)) -> 0^1_2^1_2(1(x1)) 1.51/1.57 5: 0^1_1(2(x1)) -> 0^1_2^1_2(1(4(x1))) 1.51/1.57 6: 0^1_1(2(x1)) -> 5(1(0(5(2(3(x1)))))) 1.51/1.57 7: 0^1_2^1_4(x1) -> 0^1_2^1_1(4(3(x1))) 1.51/1.57 8: 0^1_4(2(x1)) -> 4(0^1_2^1_3(x1)) 1.51/1.57 9: 0^1_4(2(x1)) -> 4(0(5(5(2(x1))))) 1.51/1.57 10: 0(0^1_4(2(x1))) -> 0(0^1_2^1_2(3(4(x1)))) 1.51/1.57 11: 0^1_1(2(2(x1))) -> 0^1_2^1_1(0^1_2(x1)) 1.51/1.57 12: 0^1_1(2(2(x1))) -> 1(3(0^1_2^1_2(x1))) 1.51/1.57 13: 0^1_1(2(4(x1))) -> 0^1_1(4(2(3(x1)))) 1.51/1.57 14: 0^1_1(2(4(x1))) -> 4(0^1_2^1_2(1(1(x1)))) 1.51/1.57 15: 0^1_1(2(4(x1))) -> 4(0(5(5(2(1(x1)))))) 1.51/1.57 16: 0^1_1(2(5(x1))) -> 3(5(5(2(1(0(x1)))))) 1.51/1.57 17: 0^1_1(4(2(x1))) -> 0(5(2(1(4(x1))))) 1.51/1.57 18: 0^1_1(5(2(x1))) -> 1(5(0^1_2^1_3(x1))) 1.51/1.57 19: 0^1_1(5(2(x1))) -> 0^1_2^1_2(1(0(5(x1)))) 1.51/1.57 20: 0^1_1(5(2(x1))) -> 5(5(0^1_2^1_1(3(x1)))) 1.51/1.57 21: 0^1_2^1_4(2(x1)) -> 0(5(4(3(2(2(x1)))))) 1.51/1.57 22: 0^1_3(1(2(x1))) -> 0^1_2^1_1(3(2(x1))) 1.51/1.57 23: 0^1_3(1(2(x1))) -> 1(0^1_2(5(3(x1)))) 1.51/1.57 24: 0^1_3(1(2(x1))) -> 1(5(0^1_2^1_3(x1))) 1.51/1.57 25: 0^1_3(1(2(x1))) -> 3(0^1_2^1_2(1(x1))) 1.51/1.57 26: 0^1_3(1(2(x1))) -> 3(2(2(1(0(x1))))) 1.51/1.57 27: 0^1_3(1(2(x1))) -> 0^1_3(2(3(1(3(x1))))) 1.51/1.57 28: 0^1_3(4(2(x1))) -> 0^1_2^1_2(3(4(x1))) 1.51/1.57 29: 5(0^1_1(2(x1))) -> 1(3(2(5(0(x1))))) 1.51/1.57 30: 5(0^1_1(2(x1))) -> 5(0^1_2^1_1(3(3(x1)))) 1.51/1.57 31: 0^1_1(1(2(5(x1)))) -> 5(0^1_2(5(1(1(x1))))) 1.51/1.57 32: 0^1_2^1_3(4(2(x1))) -> 3(2(2(3(4(0(x1)))))) 1.51/1.57 33: 0^1_3(1(2(5(x1)))) -> 2(3(1(3(0(5(x1)))))) 1.51/1.57 34: 0^1_3(1(5(2(x1)))) -> 0^1_3(2(5(1(2(x1))))) 1.51/1.57 35: 0^1_3(4(1(4(x1)))) -> 0(5(3(1(4(4(x1)))))) 1.51/1.57 36: 0^1_3(5(1(2(x1)))) -> 5(5(3(2(1(0(x1)))))) 1.51/1.57 37: 0^1_4(0^1_4(2(x1))) -> 4(4(0(0^1_2^1_2(x1)))) 1.51/1.57 38: 0^1_4(1(1(2(x1)))) -> 3(1(4(0^1_2^1_1(x1)))) 1.51/1.57 39: 0^1_4(1(2(2(x1)))) -> 4(1(0^1_2^1_2(3(x1)))) 1.51/1.57 40: 0^1_4(1(2(5(x1)))) -> 3(4(1(0^1_2(5(x1))))) 1.51/1.57 41: 0^1_4(2(1(2(x1)))) -> 4(1(3(2(0^1_2(x1))))) 1.51/1.57 42: 0^1_4(2(1(4(x1)))) -> 0^1_2^1_1(4(4(4(x1)))) 1.51/1.57 43: 0^1_4(2(5(2(x1)))) -> 5(4(3(2(2(0(x1)))))) 1.51/1.57 44: 0^1_4(5(1(2(x1)))) -> 1(4(2(0(5(5(x1)))))) 1.51/1.57 45: 0^1_4(5(1(2(x1)))) -> 4(0^1_2(5(1(1(x1))))) 1.51/1.57 46: 5(0^1_1(2(2(x1)))) -> 5(0^1_2^1_2(1(2(x1)))) 1.51/1.57 47: 5(0^1_2^1_4(2(x1))) -> 0^1_2^1_2(5(1(4(x1)))) 1.51/1.57 48: 5(0^1_4(4(2(x1)))) -> 0(5(2(5(4(4(x1)))))) 1.51/1.57 49: 0(2(_1)) ->= 0^1_2(_1) 1.51/1.57 50: 0(1(_1)) ->= 0^1_1(_1) 1.51/1.57 51: 0(4(_1)) ->= 0^1_4(_1) 1.51/1.57 52: 0(3(_1)) ->= 0^1_3(_1) 1.51/1.57 53: 0^1_2(2(_1)) ->= 0^1_2^1_2(_1) 1.51/1.57 54: 0^1_2(1(_1)) ->= 0^1_2^1_1(_1) 1.51/1.57 55: 0^1_2(4(_1)) ->= 0^1_2^1_4(_1) 1.51/1.57 56: 0^1_2(3(_1)) ->= 0^1_2^1_3(_1) 1.51/1.57 Number of strict rules: 48 1.51/1.57 Direct POLO(bPol) ... removes: 4 54 3 22 28 5 10 39 7 20 25 30 14 12 38 53 47 37 42 46 1.51/1.57 1 w: x1 1.51/1.57 4 w: x1 + 1 1.51/1.57 5 w: x1 1.51/1.57 3 w: x1 1.51/1.57 0^1_2^1_1 w: x1 1.51/1.57 0^1_4 w: x1 + 3 1.51/1.57 0^1_3 w: x1 + 2 1.51/1.57 0^1_2^1_4 w: x1 + 3 1.51/1.57 0 w: x1 + 2 1.51/1.57 0^1_2^1_2 w: x1 1.51/1.57 0^1_2^1_3 w: x1 + 2 1.51/1.57 0^1_1 w: x1 + 2 1.51/1.57 2 w: x1 1.51/1.57 0^1_2 w: x1 + 2 1.51/1.57 Number of strict rules: 30 1.51/1.57 Direct POLO(bPol) ... removes: 18 15 8 16 36 26 19 32 44 33 56 45 23 24 11 9 40 6 41 29 43 2 1.51/1.57 1 w: x1 + 2 1.51/1.57 4 w: x1 + 5 1.51/1.57 5 w: x1 1.51/1.57 3 w: x1 1.51/1.57 0^1_2^1_1 w: x1 + 1 1.51/1.57 0^1_4 w: 2 * x1 + 14 1.51/1.57 0^1_3 w: 2 * x1 + 4 1.51/1.57 0^1_2^1_4 w: 2 * x1 + 14 1.51/1.57 0 w: 2 * x1 + 4 1.51/1.57 0^1_2^1_2 w: x1 + 1 1.51/1.57 0^1_2^1_3 w: 2 * x1 + 3 1.51/1.57 0^1_1 w: 2 * x1 + 8 1.51/1.57 2 w: x1 1.51/1.57 0^1_2 w: 2 * x1 + 4 1.51/1.57 Number of strict rules: 9 1.51/1.57 Direct POLO(bPol) ... removes: 52 35 1.51/1.57 1 w: x1 + 2 1.51/1.57 4 w: 2 * x1 + 1 1.51/1.57 5 w: x1 1.51/1.57 3 w: x1 1.51/1.57 0^1_2^1_1 w: 2 * x1 + 6 1.51/1.57 0^1_4 w: 2 * x1 + 4 1.51/1.57 0^1_3 w: x1 + 2 1.51/1.57 0^1_2^1_4 w: 2 * x1 + 4 1.51/1.57 0 w: x1 + 3 1.51/1.57 0^1_2^1_2 w: 2 * x1 + 4 1.51/1.57 0^1_2^1_3 w: x1 + 6 1.51/1.57 0^1_1 w: x1 + 5 1.51/1.57 2 w: x1 1.51/1.57 0^1_2 w: x1 + 3 1.51/1.57 Number of strict rules: 8 1.51/1.57 Direct POLO(bPol) ... failed. 1.51/1.57 Dependency Pairs: 1.51/1.57 #1: #5(0^1_4(4(2(x1)))) -> #0(5(2(5(4(4(x1)))))) 1.51/1.57 #2: #5(0^1_4(4(2(x1)))) -> #5(2(5(4(4(x1))))) 1.51/1.57 #3: #5(0^1_4(4(2(x1)))) -> #5(4(4(x1))) 1.51/1.57 #4: #0^1_2(4(_1)) ->? #0^1_2^1_4(_1) 1.51/1.57 #5: #0^1_1(2(4(x1))) -> #0^1_1(4(2(3(x1)))) 1.51/1.57 #6: #0^1_1(1(2(5(x1)))) -> #5(0^1_2(5(1(1(x1))))) 1.51/1.57 #7: #0^1_1(1(2(5(x1)))) -> #0^1_2(5(1(1(x1)))) 1.51/1.57 #8: #0^1_1(1(2(5(x1)))) -> #5(1(1(x1))) 1.51/1.57 #9: #0(2(_1)) ->? #0^1_2(_1) 1.51/1.57 #10: #0^1_3(1(5(2(x1)))) -> #0^1_3(2(5(1(2(x1))))) 1.51/1.57 #11: #0^1_3(1(5(2(x1)))) -> #5(1(2(x1))) 1.51/1.57 #12: #0^1_3(1(2(x1))) -> #0^1_3(2(3(1(3(x1))))) 1.51/1.57 #13: #0^1_1(4(2(x1))) -> #0(5(2(1(4(x1))))) 1.51/1.57 #14: #0^1_1(4(2(x1))) -> #5(2(1(4(x1)))) 1.51/1.57 #15: #0^1_2^1_4(2(x1)) -> #0(5(4(3(2(2(x1)))))) 1.51/1.57 #16: #0^1_2^1_4(2(x1)) -> #5(4(3(2(2(x1))))) 1.51/1.57 #17: #0^1_1(2(x1)) -> #0^1_1(3(2(x1))) 1.51/1.57 #18: #0(1(_1)) ->? #0^1_1(_1) 1.51/1.57 Number of SCCs: 0, DPs: 0 1.51/1.57 EOF