1.25/1.27 YES 1.25/1.27 Input TRS: 1.25/1.27 1: 0(1(2(2(x1)))) -> 0(1(0(2(2(x1))))) 1.25/1.27 2: 0(1(2(2(x1)))) -> 0(1(2(3(2(x1))))) 1.25/1.27 3: 0(1(2(2(x1)))) -> 0(2(2(1(3(x1))))) 1.25/1.27 4: 0(1(2(2(x1)))) -> 1(0(3(2(2(x1))))) 1.25/1.27 5: 0(1(2(2(x1)))) -> 1(2(0(3(2(x1))))) 1.25/1.27 6: 0(1(2(2(x1)))) -> 1(3(0(2(2(x1))))) 1.25/1.27 7: 0(1(2(2(x1)))) -> 1(3(2(0(2(x1))))) 1.25/1.27 8: 0(1(2(2(x1)))) -> 0(1(0(4(2(2(x1)))))) 1.25/1.27 9: 0(1(2(2(x1)))) -> 0(2(1(3(2(3(x1)))))) 1.25/1.27 10: 0(1(2(2(x1)))) -> 1(2(1(0(4(2(x1)))))) 1.25/1.27 11: 0(1(2(2(x1)))) -> 1(5(0(4(2(2(x1)))))) 1.25/1.27 12: 0(1(2(2(x1)))) -> 2(0(3(1(3(2(x1)))))) 1.25/1.27 13: 0(1(2(2(x1)))) -> 2(1(1(0(4(2(x1)))))) 1.25/1.27 14: 0(1(2(2(x1)))) -> 2(1(3(0(2(0(x1)))))) 1.25/1.27 15: 0(1(2(2(x1)))) -> 2(1(3(3(2(0(x1)))))) 1.25/1.27 16: 0(1(2(2(x1)))) -> 2(1(5(3(0(2(x1)))))) 1.25/1.27 17: 0(1(2(2(x1)))) -> 2(2(1(3(0(5(x1)))))) 1.25/1.27 18: 0(1(2(2(x1)))) -> 2(4(1(3(2(0(x1)))))) 1.25/1.27 19: 0(1(4(5(x1)))) -> 1(5(0(4(1(x1))))) 1.25/1.27 20: 0(1(4(5(x1)))) -> 5(0(4(1(5(x1))))) 1.25/1.27 21: 0(1(4(5(x1)))) -> 5(4(1(5(0(x1))))) 1.25/1.27 22: 0(1(4(5(x1)))) -> 1(1(5(0(4(1(x1)))))) 1.25/1.27 23: 0(1(4(5(x1)))) -> 5(4(1(5(5(0(x1)))))) 1.25/1.27 24: 5(1(2(2(x1)))) -> 1(0(2(2(5(x1))))) 1.25/1.27 25: 5(1(2(2(x1)))) -> 1(3(5(2(2(x1))))) 1.25/1.27 26: 5(1(2(2(x1)))) -> 1(5(2(3(2(x1))))) 1.25/1.27 27: 5(1(2(2(x1)))) -> 1(5(0(2(2(3(x1)))))) 1.25/1.27 28: 5(1(2(2(x1)))) -> 2(1(0(3(2(5(x1)))))) 1.25/1.27 29: 5(1(2(2(x1)))) -> 3(1(3(5(2(2(x1)))))) 1.25/1.27 30: 5(1(2(2(x1)))) -> 4(1(3(2(2(5(x1)))))) 1.25/1.27 31: 5(1(2(2(x1)))) -> 5(1(0(4(2(2(x1)))))) 1.25/1.27 32: 5(1(2(2(x1)))) -> 5(1(2(0(4(2(x1)))))) 1.25/1.27 33: 0(1(1(4(5(x1))))) -> 3(1(0(4(1(5(x1)))))) 1.25/1.27 34: 0(1(2(2(2(x1))))) -> 1(0(2(2(5(2(x1)))))) 1.25/1.27 35: 0(1(2(2(5(x1))))) -> 1(5(0(4(2(2(x1)))))) 1.25/1.27 36: 0(1(2(4(5(x1))))) -> 2(5(1(0(4(5(x1)))))) 1.25/1.27 37: 0(1(4(5(2(x1))))) -> 1(0(4(2(0(5(x1)))))) 1.25/1.27 38: 0(1(4(5(5(x1))))) -> 5(0(4(0(1(5(x1)))))) 1.25/1.27 39: 0(1(5(4(5(x1))))) -> 1(5(0(4(1(5(x1)))))) 1.25/1.27 40: 0(5(1(2(2(x1))))) -> 0(1(3(2(5(2(x1)))))) 1.25/1.27 41: 3(3(1(2(2(x1))))) -> 1(3(2(0(3(2(x1)))))) 1.25/1.27 42: 3(4(4(0(5(x1))))) -> 3(5(4(5(0(4(x1)))))) 1.25/1.27 43: 5(0(1(2(2(x1))))) -> 1(3(2(0(5(2(x1)))))) 1.25/1.27 44: 5(1(2(2(5(x1))))) -> 1(5(2(3(2(5(x1)))))) 1.25/1.27 45: 5(2(1(2(2(x1))))) -> 2(1(3(5(2(2(x1)))))) 1.25/1.27 46: 5(2(4(0(5(x1))))) -> 0(4(2(5(5(5(x1)))))) 1.25/1.27 47: 5(2(4(0(5(x1))))) -> 0(4(5(4(2(5(x1)))))) 1.25/1.27 Number of strict rules: 47 1.25/1.27 Direct POLO(bPol) ... failed. 1.25/1.27 Uncurrying 3 1.25/1.27 1: 0(1(2(2(x1)))) -> 0(1(0(2(2(x1))))) 1.25/1.27 2: 0(1(2(2(x1)))) -> 0(1(2(3^1_2(x1)))) 1.25/1.27 3: 0(1(2(2(x1)))) -> 0(2(2(1(3(x1))))) 1.25/1.27 4: 0(1(2(2(x1)))) -> 1(0(3^1_2(2(x1)))) 1.25/1.27 5: 0(1(2(2(x1)))) -> 1(2(0(3^1_2(x1)))) 1.25/1.27 6: 0(1(2(2(x1)))) -> 1(3(0(2(2(x1))))) 1.25/1.27 7: 0(1(2(2(x1)))) -> 1(3^1_2(0(2(x1)))) 1.25/1.27 8: 0(1(2(2(x1)))) -> 0(1(0(4(2(2(x1)))))) 1.25/1.27 9: 0(1(2(2(x1)))) -> 0(2(1(3^1_2(3(x1))))) 1.25/1.27 10: 0(1(2(2(x1)))) -> 1(2(1(0(4(2(x1)))))) 1.25/1.27 11: 0(1(2(2(x1)))) -> 1(5(0(4(2(2(x1)))))) 1.25/1.27 12: 0(1(2(2(x1)))) -> 2(0(3^1_1(3^1_2(x1)))) 1.25/1.27 13: 0(1(2(2(x1)))) -> 2(1(1(0(4(2(x1)))))) 1.25/1.27 14: 0(1(2(2(x1)))) -> 2(1(3(0(2(0(x1)))))) 1.25/1.27 15: 0(1(2(2(x1)))) -> 2(1(3^2_2(0(x1)))) 1.25/1.27 16: 0(1(2(2(x1)))) -> 2(1(5(3(0(2(x1)))))) 1.25/1.27 17: 0(1(2(2(x1)))) -> 2(2(1(3(0(5(x1)))))) 1.25/1.27 18: 0(1(2(2(x1)))) -> 2(4(1(3^1_2(0(x1))))) 1.25/1.27 19: 0(1(4(5(x1)))) -> 1(5(0(4(1(x1))))) 1.25/1.27 20: 0(1(4(5(x1)))) -> 5(0(4(1(5(x1))))) 1.25/1.27 21: 0(1(4(5(x1)))) -> 5(4(1(5(0(x1))))) 1.25/1.27 22: 0(1(4(5(x1)))) -> 1(1(5(0(4(1(x1)))))) 1.25/1.27 23: 0(1(4(5(x1)))) -> 5(4(1(5(5(0(x1)))))) 1.25/1.27 24: 5(1(2(2(x1)))) -> 1(0(2(2(5(x1))))) 1.25/1.27 25: 5(1(2(2(x1)))) -> 1(3(5(2(2(x1))))) 1.25/1.27 26: 5(1(2(2(x1)))) -> 1(5(2(3^1_2(x1)))) 1.25/1.27 27: 5(1(2(2(x1)))) -> 1(5(0(2(2(3(x1)))))) 1.25/1.27 28: 5(1(2(2(x1)))) -> 2(1(0(3^1_2(5(x1))))) 1.25/1.27 29: 5(1(2(2(x1)))) -> 3^1_1(3(5(2(2(x1))))) 1.25/1.27 30: 5(1(2(2(x1)))) -> 4(1(3^1_2(2(5(x1))))) 1.25/1.27 31: 5(1(2(2(x1)))) -> 5(1(0(4(2(2(x1)))))) 1.25/1.27 32: 5(1(2(2(x1)))) -> 5(1(2(0(4(2(x1)))))) 1.25/1.27 33: 0(1(1(4(5(x1))))) -> 3^1_1(0(4(1(5(x1))))) 1.25/1.27 34: 0(1(2(2(2(x1))))) -> 1(0(2(2(5(2(x1)))))) 1.25/1.27 35: 0(1(2(2(5(x1))))) -> 1(5(0(4(2(2(x1)))))) 1.25/1.27 36: 0(1(2(4(5(x1))))) -> 2(5(1(0(4(5(x1)))))) 1.25/1.27 37: 0(1(4(5(2(x1))))) -> 1(0(4(2(0(5(x1)))))) 1.25/1.27 38: 0(1(4(5(5(x1))))) -> 5(0(4(0(1(5(x1)))))) 1.25/1.27 39: 0(1(5(4(5(x1))))) -> 1(5(0(4(1(5(x1)))))) 1.25/1.27 40: 0(5(1(2(2(x1))))) -> 0(1(3^1_2(5(2(x1))))) 1.25/1.27 41: 3^2_1(2(2(x1))) -> 1(3^1_2(0(3^1_2(x1)))) 1.25/1.27 42: 3^1_4(4(0(5(x1)))) -> 3(5(4(5(0(4(x1)))))) 1.25/1.27 43: 5(0(1(2(2(x1))))) -> 1(3^1_2(0(5(2(x1))))) 1.25/1.27 44: 5(1(2(2(5(x1))))) -> 1(5(2(3^1_2(5(x1))))) 1.25/1.27 45: 5(2(1(2(2(x1))))) -> 2(1(3(5(2(2(x1)))))) 1.25/1.27 46: 5(2(4(0(5(x1))))) -> 0(4(2(5(5(5(x1)))))) 1.25/1.27 47: 5(2(4(0(5(x1))))) -> 0(4(5(4(2(5(x1)))))) 1.25/1.27 48: 3(2(_1)) ->= 3^1_2(_1) 1.25/1.27 49: 3(3^1_2(_1)) ->= 3^2_2(_1) 1.25/1.27 50: 3(1(_1)) ->= 3^1_1(_1) 1.25/1.27 51: 3(3^1_1(_1)) ->= 3^2_1(_1) 1.25/1.27 52: 3(4(_1)) ->= 3^1_4(_1) 1.25/1.27 Number of strict rules: 47 1.25/1.27 Direct POLO(bPol) ... removes: 18 4 15 26 28 44 5 7 49 30 12 9 40 48 41 43 2 1.25/1.27 1 w: x1 1.25/1.27 4 w: x1 1.25/1.27 5 w: x1 1.25/1.27 3 w: x1 1.25/1.27 3^1_4 w: x1 1.25/1.27 0 w: x1 1.25/1.27 2 w: x1 + 3 1.25/1.27 3^1_1 w: x1 1.25/1.27 3^1_2 w: x1 + 2 1.25/1.27 3^2_2 w: x1 + 1 1.25/1.27 3^2_1 w: x1 1.25/1.27 Number of strict rules: 32 1.25/1.27 Direct POLO(bPol) ... failed. 1.25/1.27 Dependency Pairs: 1.25/1.27 #1: #5(1(2(2(x1)))) -> #3(5(2(2(x1)))) 1.25/1.27 #2: #5(1(2(2(x1)))) -> #5(2(2(x1))) 1.25/1.27 #3: #0(1(2(2(5(x1))))) -> #5(0(4(2(2(x1))))) 1.25/1.27 #4: #0(1(2(2(5(x1))))) -> #0(4(2(2(x1)))) 1.25/1.27 #5: #5(2(4(0(5(x1))))) -> #0(4(2(5(5(5(x1)))))) 1.25/1.27 #6: #5(2(4(0(5(x1))))) -> #5(5(5(x1))) 1.25/1.27 #7: #5(2(4(0(5(x1))))) -> #5(5(x1)) 1.25/1.27 #8: #3^1_4(4(0(5(x1)))) -> #3(5(4(5(0(4(x1)))))) 1.25/1.27 #9: #3^1_4(4(0(5(x1)))) -> #5(4(5(0(4(x1))))) 1.25/1.27 #10: #3^1_4(4(0(5(x1)))) -> #5(0(4(x1))) 1.25/1.27 #11: #3^1_4(4(0(5(x1)))) -> #0(4(x1)) 1.25/1.27 #12: #0(1(4(5(2(x1))))) -> #0(4(2(0(5(x1))))) 1.25/1.27 #13: #0(1(4(5(2(x1))))) -> #0(5(x1)) 1.25/1.27 #14: #0(1(4(5(2(x1))))) -> #5(x1) 1.25/1.27 #15: #5(2(4(0(5(x1))))) -> #0(4(5(4(2(5(x1)))))) 1.25/1.27 #16: #5(2(4(0(5(x1))))) -> #5(4(2(5(x1)))) 1.25/1.27 #17: #0(1(4(5(5(x1))))) -> #5(0(4(0(1(5(x1)))))) 1.25/1.27 #18: #0(1(4(5(5(x1))))) -> #0(4(0(1(5(x1))))) 1.25/1.27 #19: #0(1(4(5(5(x1))))) -> #0(1(5(x1))) 1.25/1.27 #20: #0(1(2(2(x1)))) -> #3(0(2(2(x1)))) 1.25/1.27 #21: #0(1(2(2(x1)))) -> #0(2(2(x1))) 1.25/1.27 #22: #0(1(2(2(x1)))) -> #0(4(2(x1))) 1.25/1.27 #23: #0(1(2(2(x1)))) -> #5(0(4(2(2(x1))))) 1.25/1.27 #24: #0(1(2(2(x1)))) -> #0(4(2(2(x1)))) 1.25/1.27 #25: #5(1(2(2(x1)))) -> #0(2(2(5(x1)))) 1.25/1.27 #26: #5(1(2(2(x1)))) -> #5(x1) 1.25/1.27 #27: #0(1(4(5(x1)))) -> #5(4(1(5(5(0(x1)))))) 1.25/1.27 #28: #0(1(4(5(x1)))) -> #5(5(0(x1))) 1.25/1.27 #29: #0(1(4(5(x1)))) -> #5(0(x1)) 1.25/1.27 #30: #0(1(4(5(x1)))) -> #0(x1) 1.25/1.27 #31: #5(2(1(2(2(x1))))) -> #3(5(2(2(x1)))) 1.25/1.27 #32: #5(2(1(2(2(x1))))) -> #5(2(2(x1))) 1.25/1.27 #33: #5(1(2(2(x1)))) -> #5(1(0(4(2(2(x1)))))) 1.25/1.27 #34: #5(1(2(2(x1)))) -> #0(4(2(2(x1)))) 1.25/1.27 #35: #0(1(2(2(x1)))) -> #3(0(2(0(x1)))) 1.25/1.27 #36: #0(1(2(2(x1)))) -> #0(2(0(x1))) 1.25/1.27 #37: #0(1(2(2(x1)))) -> #0(x1) 1.25/1.27 #38: #3(4(_1)) ->? #3^1_4(_1) 1.25/1.27 #39: #5(1(2(2(x1)))) -> #3(5(2(2(x1)))) 1.25/1.27 #40: #5(1(2(2(x1)))) -> #5(2(2(x1))) 1.25/1.27 #41: #0(1(4(5(x1)))) -> #5(0(4(1(5(x1))))) 1.25/1.27 #42: #0(1(4(5(x1)))) -> #0(4(1(5(x1)))) 1.25/1.27 #43: #0(1(5(4(5(x1))))) -> #5(0(4(1(5(x1))))) 1.25/1.27 #44: #0(1(5(4(5(x1))))) -> #0(4(1(5(x1)))) 1.25/1.27 #45: #0(1(2(2(x1)))) -> #0(4(2(x1))) 1.25/1.27 #46: #0(1(1(4(5(x1))))) -> #0(4(1(5(x1)))) 1.25/1.27 #47: #0(1(4(5(x1)))) -> #5(0(4(1(x1)))) 1.25/1.27 #48: #0(1(4(5(x1)))) -> #0(4(1(x1))) 1.25/1.27 #49: #0(1(2(2(2(x1))))) -> #0(2(2(5(2(x1))))) 1.25/1.27 #50: #0(1(2(2(2(x1))))) -> #5(2(x1)) 1.25/1.27 #51: #5(1(2(2(x1)))) -> #5(0(2(2(3(x1))))) 1.25/1.27 #52: #5(1(2(2(x1)))) -> #0(2(2(3(x1)))) 1.25/1.27 #53: #5(1(2(2(x1)))) -> #3(x1) 1.25/1.27 #54: #0(1(2(2(x1)))) -> #3(0(5(x1))) 1.25/1.27 #55: #0(1(2(2(x1)))) -> #0(5(x1)) 1.25/1.27 #56: #0(1(2(2(x1)))) -> #5(x1) 1.25/1.27 #57: #0(1(4(5(x1)))) -> #5(0(4(1(x1)))) 1.25/1.27 #58: #0(1(4(5(x1)))) -> #0(4(1(x1))) 1.25/1.27 #59: #5(1(2(2(x1)))) -> #5(1(2(0(4(2(x1)))))) 1.25/1.27 #60: #5(1(2(2(x1)))) -> #0(4(2(x1))) 1.25/1.27 #61: #0(1(2(4(5(x1))))) -> #5(1(0(4(5(x1))))) 1.25/1.27 #62: #0(1(2(4(5(x1))))) -> #0(4(5(x1))) 1.25/1.27 #63: #0(1(4(5(x1)))) -> #5(4(1(5(0(x1))))) 1.25/1.27 #64: #0(1(4(5(x1)))) -> #5(0(x1)) 1.25/1.27 #65: #0(1(4(5(x1)))) -> #0(x1) 1.25/1.27 #66: #0(1(2(2(x1)))) -> #5(3(0(2(x1)))) 1.25/1.27 #67: #0(1(2(2(x1)))) -> #3(0(2(x1))) 1.25/1.27 #68: #0(1(2(2(x1)))) -> #0(2(x1)) 1.25/1.27 #69: #0(1(2(2(x1)))) -> #0(2(2(1(3(x1))))) 1.25/1.27 #70: #0(1(2(2(x1)))) -> #3(x1) 1.25/1.27 #71: #0(1(2(2(x1)))) -> #0(1(0(2(2(x1))))) 1.25/1.27 #72: #0(1(2(2(x1)))) -> #0(2(2(x1))) 1.25/1.27 #73: #0(1(2(2(x1)))) -> #0(1(0(4(2(2(x1)))))) 1.25/1.27 #74: #0(1(2(2(x1)))) -> #0(4(2(2(x1)))) 1.25/1.27 Number of SCCs: 2, DPs: 4 1.25/1.27 SCC { #26 } 1.25/1.27 POLO(Sum)... succeeded. 1.25/1.27 #0 w: 0 1.25/1.27 1 w: x1 + 1 1.25/1.27 4 w: 0 1.25/1.27 5 w: 0 1.25/1.27 3 w: 0 1.25/1.27 3^1_4 w: 0 1.25/1.27 0 w: 0 1.25/1.27 #3 w: 0 1.25/1.27 #5 w: x1 1.25/1.27 2 w: x1 + 1 1.25/1.27 3^1_1 w: 0 1.25/1.27 3^1_2 w: 0 1.25/1.27 3^2_2 w: 0 1.25/1.27 #3^1_4 w: 0 1.25/1.27 3^2_1 w: 0 1.25/1.27 USABLE RULES: { } 1.25/1.27 Removed DPs: #26 1.25/1.27 Number of SCCs: 1, DPs: 3 1.25/1.27 SCC { #30 #37 #65 } 1.25/1.27 POLO(Sum)... succeeded. 1.25/1.27 #0 w: x1 1.25/1.27 1 w: x1 + 1 1.25/1.27 4 w: x1 1.25/1.27 5 w: x1 + 1 1.25/1.27 3 w: 0 1.25/1.27 3^1_4 w: 0 1.25/1.27 0 w: 0 1.25/1.27 #3 w: 0 1.25/1.27 #5 w: 0 1.25/1.27 2 w: x1 + 1 1.25/1.27 3^1_1 w: 0 1.25/1.27 3^1_2 w: 0 1.25/1.27 3^2_2 w: 0 1.25/1.27 #3^1_4 w: 0 1.25/1.27 3^2_1 w: 0 1.25/1.27 USABLE RULES: { } 1.25/1.27 Removed DPs: #30 #37 #65 1.25/1.27 Number of SCCs: 0, DPs: 0 1.25/1.27 EOF