10.55/8.87 YES 10.55/8.87 Input TRS: 10.55/8.87 1: 0(1(1(x1))) -> 0(2(1(1(x1)))) 10.55/8.87 2: 0(1(1(x1))) -> 0(0(2(1(1(x1))))) 10.55/8.87 3: 0(1(1(x1))) -> 0(2(1(2(1(x1))))) 10.55/8.87 4: 0(1(1(x1))) -> 2(1(0(2(1(x1))))) 10.55/8.87 5: 3(0(1(x1))) -> 1(3(0(0(2(4(x1)))))) 10.55/8.87 6: 3(5(1(x1))) -> 1(3(4(5(x1)))) 10.55/8.87 7: 3(5(1(x1))) -> 2(4(5(3(1(x1))))) 10.55/8.87 8: 5(1(3(x1))) -> 5(3(1(2(x1)))) 10.55/8.87 9: 0(1(0(1(x1)))) -> 1(1(0(0(2(4(x1)))))) 10.55/8.87 10: 0(1(2(3(x1)))) -> 3(1(5(0(2(x1))))) 10.55/8.87 11: 0(1(2(3(x1)))) -> 0(3(1(2(1(1(x1)))))) 10.55/8.87 12: 0(1(4(1(x1)))) -> 0(2(1(2(4(1(x1)))))) 10.55/8.87 13: 0(1(4(1(x1)))) -> 4(0(0(2(1(1(x1)))))) 10.55/8.87 14: 0(1(5(1(x1)))) -> 0(0(2(1(1(5(x1)))))) 10.55/8.87 15: 0(4(5(1(x1)))) -> 0(1(3(4(5(x1))))) 10.55/8.87 16: 3(2(0(1(x1)))) -> 1(3(0(2(4(5(x1)))))) 10.55/8.87 17: 3(5(1(1(x1)))) -> 1(3(4(5(1(x1))))) 10.55/8.87 18: 3(5(1(1(x1)))) -> 1(5(3(1(2(x1))))) 10.55/8.87 19: 3(5(1(3(x1)))) -> 3(5(3(1(2(x1))))) 10.55/8.87 20: 3(5(4(1(x1)))) -> 4(1(3(4(5(x1))))) 10.55/8.87 21: 5(1(2(3(x1)))) -> 5(5(3(1(2(x1))))) 10.55/8.87 22: 5(2(0(1(x1)))) -> 5(3(1(0(2(4(x1)))))) 10.55/8.87 23: 5(4(3(3(x1)))) -> 3(1(3(4(5(x1))))) 10.55/8.87 24: 5(5(0(1(x1)))) -> 1(0(2(4(5(5(x1)))))) 10.55/8.87 25: 0(1(2(0(1(x1))))) -> 0(3(0(2(1(1(x1)))))) 10.55/8.87 26: 0(1(2(2(1(x1))))) -> 0(2(1(2(1(3(x1)))))) 10.55/8.87 27: 0(3(0(5(1(x1))))) -> 0(3(4(5(0(1(x1)))))) 10.55/8.87 28: 0(3(4(2(3(x1))))) -> 0(5(3(4(3(2(x1)))))) 10.55/8.87 29: 0(3(5(4(1(x1))))) -> 0(5(2(4(3(1(x1)))))) 10.55/8.87 30: 0(4(1(2(3(x1))))) -> 0(3(2(4(5(1(x1)))))) 10.55/8.87 31: 0(4(1(2(3(x1))))) -> 4(3(1(0(0(2(x1)))))) 10.55/8.87 32: 0(4(5(5(1(x1))))) -> 2(4(5(5(0(1(x1)))))) 10.55/8.87 33: 0(5(1(0(1(x1))))) -> 0(1(5(5(0(1(x1)))))) 10.55/8.87 34: 0(5(3(2(1(x1))))) -> 0(0(2(5(3(1(x1)))))) 10.55/8.87 35: 3(0(1(2(3(x1))))) -> 0(2(3(4(3(1(x1)))))) 10.55/8.87 36: 3(0(1(2(3(x1))))) -> 1(1(3(3(0(2(x1)))))) 10.55/8.87 37: 3(0(1(2(3(x1))))) -> 1(2(3(3(0(2(x1)))))) 10.55/8.87 38: 3(0(4(1(1(x1))))) -> 0(0(1(3(4(1(x1)))))) 10.55/8.87 39: 3(2(4(1(3(x1))))) -> 4(3(4(3(1(2(x1)))))) 10.55/8.87 40: 3(3(4(1(1(x1))))) -> 1(3(4(5(3(1(x1)))))) 10.55/8.87 41: 3(3(5(1(1(x1))))) -> 3(1(4(5(3(1(x1)))))) 10.55/8.87 42: 3(5(4(1(3(x1))))) -> 1(4(5(3(1(3(x1)))))) 10.55/8.87 43: 3(5(4(4(1(x1))))) -> 4(1(4(3(4(5(x1)))))) 10.55/8.87 44: 5(2(4(2(3(x1))))) -> 3(2(4(5(3(2(x1)))))) 10.55/8.87 45: 5(4(2(0(1(x1))))) -> 5(1(2(0(2(4(x1)))))) 10.55/8.87 Number of strict rules: 45 10.55/8.87 Direct POLO(bPol) ... failed. 10.55/8.87 Uncurrying ... failed. 10.55/8.87 Dependency Pairs: 10.55/8.87 #1: #0(1(1(x1))) -> #0(0(2(1(1(x1))))) 10.55/8.87 #2: #0(1(1(x1))) -> #0(2(1(1(x1)))) 10.55/8.87 #3: #3(5(4(4(1(x1))))) -> #3(4(5(x1))) 10.55/8.87 #4: #3(5(4(4(1(x1))))) -> #5(x1) 10.55/8.87 #5: #0(3(5(4(1(x1))))) -> #0(5(2(4(3(1(x1)))))) 10.55/8.87 #6: #0(3(5(4(1(x1))))) -> #5(2(4(3(1(x1))))) 10.55/8.87 #7: #0(3(5(4(1(x1))))) -> #3(1(x1)) 10.55/8.87 #8: #3(0(1(2(3(x1))))) -> #0(2(3(4(3(1(x1)))))) 10.55/8.87 #9: #3(0(1(2(3(x1))))) -> #3(4(3(1(x1)))) 10.55/8.87 #10: #3(0(1(2(3(x1))))) -> #3(1(x1)) 10.55/8.87 #11: #3(5(4(1(3(x1))))) -> #5(3(1(3(x1)))) 10.55/8.87 #12: #3(5(4(1(3(x1))))) -> #3(1(3(x1))) 10.55/8.87 #13: #3(3(5(1(1(x1))))) -> #3(1(4(5(3(1(x1)))))) 10.55/8.87 #14: #3(3(5(1(1(x1))))) -> #5(3(1(x1))) 10.55/8.87 #15: #3(3(5(1(1(x1))))) -> #3(1(x1)) 10.55/8.87 #16: #3(0(1(2(3(x1))))) -> #3(3(0(2(x1)))) 10.55/8.87 #17: #3(0(1(2(3(x1))))) -> #3(0(2(x1))) 10.55/8.87 #18: #3(0(1(2(3(x1))))) -> #0(2(x1)) 10.55/8.87 #19: #3(0(4(1(1(x1))))) -> #0(0(1(3(4(1(x1)))))) 10.55/8.87 #20: #3(0(4(1(1(x1))))) -> #0(1(3(4(1(x1))))) 10.55/8.87 #21: #3(0(4(1(1(x1))))) -> #3(4(1(x1))) 10.55/8.87 #22: #3(5(1(x1))) -> #3(4(5(x1))) 10.55/8.87 #23: #3(5(1(x1))) -> #5(x1) 10.55/8.87 #24: #3(3(4(1(1(x1))))) -> #3(4(5(3(1(x1))))) 10.55/8.87 #25: #3(3(4(1(1(x1))))) -> #5(3(1(x1))) 10.55/8.87 #26: #3(3(4(1(1(x1))))) -> #3(1(x1)) 10.55/8.87 #27: #0(1(4(1(x1)))) -> #0(0(2(1(1(x1))))) 10.55/8.87 #28: #0(1(4(1(x1)))) -> #0(2(1(1(x1)))) 10.55/8.87 #29: #0(1(0(1(x1)))) -> #0(0(2(4(x1)))) 10.55/8.87 #30: #0(1(0(1(x1)))) -> #0(2(4(x1))) 10.55/8.87 #31: #0(1(2(3(x1)))) -> #0(3(1(2(1(1(x1)))))) 10.55/8.87 #32: #0(1(2(3(x1)))) -> #3(1(2(1(1(x1))))) 10.55/8.87 #33: #5(5(0(1(x1)))) -> #0(2(4(5(5(x1))))) 10.55/8.87 #34: #5(5(0(1(x1)))) -> #5(5(x1)) 10.55/8.87 #35: #5(5(0(1(x1)))) -> #5(x1) 10.55/8.87 #36: #5(4(3(3(x1)))) -> #3(1(3(4(5(x1))))) 10.55/8.87 #37: #5(4(3(3(x1)))) -> #3(4(5(x1))) 10.55/8.87 #38: #5(4(3(3(x1)))) -> #5(x1) 10.55/8.87 #39: #5(4(2(0(1(x1))))) -> #5(1(2(0(2(4(x1)))))) 10.55/8.87 #40: #5(4(2(0(1(x1))))) -> #0(2(4(x1))) 10.55/8.87 #41: #0(1(4(1(x1)))) -> #0(2(1(2(4(1(x1)))))) 10.55/8.87 #42: #0(4(1(2(3(x1))))) -> #3(1(0(0(2(x1))))) 10.55/8.87 #43: #0(4(1(2(3(x1))))) -> #0(0(2(x1))) 10.55/8.87 #44: #0(4(1(2(3(x1))))) -> #0(2(x1)) 10.55/8.87 #45: #0(1(5(1(x1)))) -> #0(0(2(1(1(5(x1)))))) 10.55/8.87 #46: #0(1(5(1(x1)))) -> #0(2(1(1(5(x1))))) 10.55/8.87 #47: #0(1(5(1(x1)))) -> #5(x1) 10.55/8.87 #48: #0(4(1(2(3(x1))))) -> #0(3(2(4(5(1(x1)))))) 10.55/8.87 #49: #0(4(1(2(3(x1))))) -> #3(2(4(5(1(x1))))) 10.55/8.87 #50: #0(4(1(2(3(x1))))) -> #5(1(x1)) 10.55/8.87 #51: #0(1(2(0(1(x1))))) -> #0(3(0(2(1(1(x1)))))) 10.55/8.87 #52: #0(1(2(0(1(x1))))) -> #3(0(2(1(1(x1))))) 10.55/8.87 #53: #0(1(2(0(1(x1))))) -> #0(2(1(1(x1)))) 10.55/8.87 #54: #3(5(4(1(x1)))) -> #3(4(5(x1))) 10.55/8.87 #55: #3(5(4(1(x1)))) -> #5(x1) 10.55/8.87 #56: #3(5(1(x1))) -> #5(3(1(x1))) 10.55/8.87 #57: #3(5(1(x1))) -> #3(1(x1)) 10.55/8.87 #58: #3(2(4(1(3(x1))))) -> #3(4(3(1(2(x1))))) 10.55/8.87 #59: #3(2(4(1(3(x1))))) -> #3(1(2(x1))) 10.55/8.87 #60: #0(1(2(3(x1)))) -> #3(1(5(0(2(x1))))) 10.55/8.87 #61: #0(1(2(3(x1)))) -> #5(0(2(x1))) 10.55/8.87 #62: #0(1(2(3(x1)))) -> #0(2(x1)) 10.55/8.87 #63: #0(5(1(0(1(x1))))) -> #0(1(5(5(0(1(x1)))))) 10.55/8.87 #64: #0(5(1(0(1(x1))))) -> #5(5(0(1(x1)))) 10.55/8.87 #65: #0(5(1(0(1(x1))))) -> #5(0(1(x1))) 10.55/8.87 #66: #3(0(1(x1))) -> #3(0(0(2(4(x1))))) 10.55/8.87 #67: #3(0(1(x1))) -> #0(0(2(4(x1)))) 10.55/8.87 #68: #3(0(1(x1))) -> #0(2(4(x1))) 10.55/8.87 #69: #5(2(4(2(3(x1))))) -> #3(2(4(5(3(2(x1)))))) 10.55/8.87 #70: #5(2(4(2(3(x1))))) -> #5(3(2(x1))) 10.55/8.87 #71: #5(2(4(2(3(x1))))) -> #3(2(x1)) 10.55/8.87 #72: #0(3(4(2(3(x1))))) -> #0(5(3(4(3(2(x1)))))) 10.55/8.87 #73: #0(3(4(2(3(x1))))) -> #5(3(4(3(2(x1))))) 10.55/8.87 #74: #0(3(4(2(3(x1))))) -> #3(4(3(2(x1)))) 10.55/8.87 #75: #0(3(4(2(3(x1))))) -> #3(2(x1)) 10.55/8.87 #76: #5(2(0(1(x1)))) -> #5(3(1(0(2(4(x1)))))) 10.55/8.87 #77: #5(2(0(1(x1)))) -> #3(1(0(2(4(x1))))) 10.55/8.87 #78: #5(2(0(1(x1)))) -> #0(2(4(x1))) 10.55/8.87 #79: #0(5(3(2(1(x1))))) -> #0(0(2(5(3(1(x1)))))) 10.55/8.87 #80: #0(5(3(2(1(x1))))) -> #0(2(5(3(1(x1))))) 10.55/8.87 #81: #0(5(3(2(1(x1))))) -> #5(3(1(x1))) 10.55/8.87 #82: #0(5(3(2(1(x1))))) -> #3(1(x1)) 10.55/8.87 #83: #0(3(0(5(1(x1))))) -> #0(3(4(5(0(1(x1)))))) 10.55/8.87 #84: #0(3(0(5(1(x1))))) -> #3(4(5(0(1(x1))))) 10.55/8.87 #85: #0(3(0(5(1(x1))))) -> #5(0(1(x1))) 10.55/8.87 #86: #0(3(0(5(1(x1))))) -> #0(1(x1)) 10.55/8.87 #87: #3(5(1(1(x1)))) -> #3(4(5(1(x1)))) 10.55/8.87 #88: #3(5(1(1(x1)))) -> #5(1(x1)) 10.55/8.87 #89: #0(4(5(5(1(x1))))) -> #5(5(0(1(x1)))) 10.55/8.87 #90: #0(4(5(5(1(x1))))) -> #5(0(1(x1))) 10.55/8.87 #91: #0(4(5(5(1(x1))))) -> #0(1(x1)) 10.55/8.87 #92: #3(5(1(3(x1)))) -> #3(5(3(1(2(x1))))) 10.55/8.87 #93: #3(5(1(3(x1)))) -> #5(3(1(2(x1)))) 10.55/8.87 #94: #3(5(1(3(x1)))) -> #3(1(2(x1))) 10.55/8.87 #95: #0(1(2(2(1(x1))))) -> #0(2(1(2(1(3(x1)))))) 10.55/8.87 #96: #0(1(2(2(1(x1))))) -> #3(x1) 10.55/8.87 #97: #3(0(1(2(3(x1))))) -> #3(3(0(2(x1)))) 10.55/8.87 #98: #3(0(1(2(3(x1))))) -> #3(0(2(x1))) 10.55/8.87 #99: #3(0(1(2(3(x1))))) -> #0(2(x1)) 10.55/8.87 #100: #5(1(2(3(x1)))) -> #5(5(3(1(2(x1))))) 10.55/8.87 #101: #5(1(2(3(x1)))) -> #5(3(1(2(x1)))) 10.55/8.87 #102: #5(1(2(3(x1)))) -> #3(1(2(x1))) 10.55/8.87 #103: #3(2(0(1(x1)))) -> #3(0(2(4(5(x1))))) 10.55/8.87 #104: #3(2(0(1(x1)))) -> #0(2(4(5(x1)))) 10.55/8.87 #105: #3(2(0(1(x1)))) -> #5(x1) 10.55/8.87 #106: #0(1(1(x1))) -> #0(2(1(2(1(x1))))) 10.55/8.87 #107: #0(1(1(x1))) -> #0(2(1(1(x1)))) 10.55/8.87 #108: #5(1(3(x1))) -> #5(3(1(2(x1)))) 10.55/8.87 #109: #5(1(3(x1))) -> #3(1(2(x1))) 10.55/8.87 #110: #0(4(5(1(x1)))) -> #0(1(3(4(5(x1))))) 10.55/8.87 #111: #0(4(5(1(x1)))) -> #3(4(5(x1))) 10.55/8.87 #112: #0(4(5(1(x1)))) -> #5(x1) 10.55/8.87 #113: #0(1(1(x1))) -> #0(2(1(x1))) 10.55/8.87 #114: #3(5(1(1(x1)))) -> #5(3(1(2(x1)))) 10.55/8.87 #115: #3(5(1(1(x1)))) -> #3(1(2(x1))) 10.55/8.87 Number of SCCs: 1, DPs: 5 10.55/8.87 SCC { #34 #35 #38 #71 #105 } 10.55/8.87 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. 10.55/8.87 #0 w: [0;0] 10.55/8.87 1 w: [1,0;1,0] * x1 + [0;2] 10.55/8.87 4 w: [1,0;1,0] * x1 + [0;2] 10.55/8.87 5 w: [1,0;1,0] * x1 + [0;2] 10.55/8.87 3 w: [1,0;1,0] * x1 + [0;2] 10.55/8.87 0 w: [0,1;0,1] * x1 10.55/8.87 #3 w: [1,0;0,0] * x1 + [0;1] 10.55/8.87 #5 w: [1,0;0,0] * x1 + [1;1] 10.55/8.87 2 w: [1,0;1,0] * x1 10.55/8.87 USABLE RULES: { 1..45 } 10.55/8.87 Removed DPs: #34 #35 #71 #105 10.55/8.87 Number of SCCs: 1, DPs: 1 10.55/8.87 SCC { #38 } 10.55/8.87 POLO(Sum)... succeeded. 10.55/8.87 #0 w: 0 10.55/8.87 1 w: 1 10.55/8.87 4 w: x1 10.55/8.87 5 w: 3 10.55/8.87 3 w: x1 + 1 10.55/8.87 0 w: 2 10.55/8.87 #3 w: 0 10.55/8.87 #5 w: x1 10.55/8.87 2 w: 2 10.55/8.87 USABLE RULES: { 1..45 } 10.55/8.87 Removed DPs: #38 10.55/8.87 Number of SCCs: 0, DPs: 0 10.55/8.87 EOF