YES Input TRS: 1: 0(1(1(x1))) -> 0(2(1(1(x1)))) 2: 0(1(1(x1))) -> 0(0(2(1(1(x1))))) 3: 0(1(1(x1))) -> 0(2(1(2(1(x1))))) 4: 0(1(1(x1))) -> 2(1(0(2(1(x1))))) 5: 3(0(1(x1))) -> 1(3(0(0(2(4(x1)))))) 6: 3(5(1(x1))) -> 1(3(4(5(x1)))) 7: 3(5(1(x1))) -> 2(4(5(3(1(x1))))) 8: 5(1(3(x1))) -> 5(3(1(2(x1)))) 9: 0(1(0(1(x1)))) -> 1(1(0(0(2(4(x1)))))) 10: 0(1(2(3(x1)))) -> 3(1(5(0(2(x1))))) 11: 0(1(2(3(x1)))) -> 0(3(1(2(1(1(x1)))))) 12: 0(1(4(1(x1)))) -> 0(2(1(2(4(1(x1)))))) 13: 0(1(4(1(x1)))) -> 4(0(0(2(1(1(x1)))))) 14: 0(1(5(1(x1)))) -> 0(0(2(1(1(5(x1)))))) 15: 0(4(5(1(x1)))) -> 0(1(3(4(5(x1))))) 16: 3(2(0(1(x1)))) -> 1(3(0(2(4(5(x1)))))) 17: 3(5(1(1(x1)))) -> 1(3(4(5(1(x1))))) 18: 3(5(1(1(x1)))) -> 1(5(3(1(2(x1))))) 19: 3(5(1(3(x1)))) -> 3(5(3(1(2(x1))))) 20: 3(5(4(1(x1)))) -> 4(1(3(4(5(x1))))) 21: 5(1(2(3(x1)))) -> 5(5(3(1(2(x1))))) 22: 5(2(0(1(x1)))) -> 5(3(1(0(2(4(x1)))))) 23: 5(4(3(3(x1)))) -> 3(1(3(4(5(x1))))) 24: 5(5(0(1(x1)))) -> 1(0(2(4(5(5(x1)))))) 25: 0(1(2(0(1(x1))))) -> 0(3(0(2(1(1(x1)))))) 26: 0(1(2(2(1(x1))))) -> 0(2(1(2(1(3(x1)))))) 27: 0(3(0(5(1(x1))))) -> 0(3(4(5(0(1(x1)))))) 28: 0(3(4(2(3(x1))))) -> 0(5(3(4(3(2(x1)))))) 29: 0(3(5(4(1(x1))))) -> 0(5(2(4(3(1(x1)))))) 30: 0(4(1(2(3(x1))))) -> 0(3(2(4(5(1(x1)))))) 31: 0(4(1(2(3(x1))))) -> 4(3(1(0(0(2(x1)))))) 32: 0(4(5(5(1(x1))))) -> 2(4(5(5(0(1(x1)))))) 33: 0(5(1(0(1(x1))))) -> 0(1(5(5(0(1(x1)))))) 34: 0(5(3(2(1(x1))))) -> 0(0(2(5(3(1(x1)))))) 35: 3(0(1(2(3(x1))))) -> 0(2(3(4(3(1(x1)))))) 36: 3(0(1(2(3(x1))))) -> 1(1(3(3(0(2(x1)))))) 37: 3(0(1(2(3(x1))))) -> 1(2(3(3(0(2(x1)))))) 38: 3(0(4(1(1(x1))))) -> 0(0(1(3(4(1(x1)))))) 39: 3(2(4(1(3(x1))))) -> 4(3(4(3(1(2(x1)))))) 40: 3(3(4(1(1(x1))))) -> 1(3(4(5(3(1(x1)))))) 41: 3(3(5(1(1(x1))))) -> 3(1(4(5(3(1(x1)))))) 42: 3(5(4(1(3(x1))))) -> 1(4(5(3(1(3(x1)))))) 43: 3(5(4(4(1(x1))))) -> 4(1(4(3(4(5(x1)))))) 44: 5(2(4(2(3(x1))))) -> 3(2(4(5(3(2(x1)))))) 45: 5(4(2(0(1(x1))))) -> 5(1(2(0(2(4(x1)))))) Number of strict rules: 45 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #0(1(1(x1))) -> #0(0(2(1(1(x1))))) #2: #0(1(1(x1))) -> #0(2(1(1(x1)))) #3: #3(5(4(4(1(x1))))) -> #3(4(5(x1))) #4: #3(5(4(4(1(x1))))) -> #5(x1) #5: #0(3(5(4(1(x1))))) -> #0(5(2(4(3(1(x1)))))) #6: #0(3(5(4(1(x1))))) -> #5(2(4(3(1(x1))))) #7: #0(3(5(4(1(x1))))) -> #3(1(x1)) #8: #3(0(1(2(3(x1))))) -> #0(2(3(4(3(1(x1)))))) #9: #3(0(1(2(3(x1))))) -> #3(4(3(1(x1)))) #10: #3(0(1(2(3(x1))))) -> #3(1(x1)) #11: #3(5(4(1(3(x1))))) -> #5(3(1(3(x1)))) #12: #3(5(4(1(3(x1))))) -> #3(1(3(x1))) #13: #3(3(5(1(1(x1))))) -> #3(1(4(5(3(1(x1)))))) #14: #3(3(5(1(1(x1))))) -> #5(3(1(x1))) #15: #3(3(5(1(1(x1))))) -> #3(1(x1)) #16: #3(0(1(2(3(x1))))) -> #3(3(0(2(x1)))) #17: #3(0(1(2(3(x1))))) -> #3(0(2(x1))) #18: #3(0(1(2(3(x1))))) -> #0(2(x1)) #19: #3(0(4(1(1(x1))))) -> #0(0(1(3(4(1(x1)))))) #20: #3(0(4(1(1(x1))))) -> #0(1(3(4(1(x1))))) #21: #3(0(4(1(1(x1))))) -> #3(4(1(x1))) #22: #3(5(1(x1))) -> #3(4(5(x1))) #23: #3(5(1(x1))) -> #5(x1) #24: #3(3(4(1(1(x1))))) -> #3(4(5(3(1(x1))))) #25: #3(3(4(1(1(x1))))) -> #5(3(1(x1))) #26: #3(3(4(1(1(x1))))) -> #3(1(x1)) #27: #0(1(4(1(x1)))) -> #0(0(2(1(1(x1))))) #28: #0(1(4(1(x1)))) -> #0(2(1(1(x1)))) #29: #0(1(0(1(x1)))) -> #0(0(2(4(x1)))) #30: #0(1(0(1(x1)))) -> #0(2(4(x1))) #31: #0(1(2(3(x1)))) -> #0(3(1(2(1(1(x1)))))) #32: #0(1(2(3(x1)))) -> #3(1(2(1(1(x1))))) #33: #5(5(0(1(x1)))) -> #0(2(4(5(5(x1))))) #34: #5(5(0(1(x1)))) -> #5(5(x1)) #35: #5(5(0(1(x1)))) -> #5(x1) #36: #5(4(3(3(x1)))) -> #3(1(3(4(5(x1))))) #37: #5(4(3(3(x1)))) -> #3(4(5(x1))) #38: #5(4(3(3(x1)))) -> #5(x1) #39: #5(4(2(0(1(x1))))) -> #5(1(2(0(2(4(x1)))))) #40: #5(4(2(0(1(x1))))) -> #0(2(4(x1))) #41: #0(1(4(1(x1)))) -> #0(2(1(2(4(1(x1)))))) #42: #0(4(1(2(3(x1))))) -> #3(1(0(0(2(x1))))) #43: #0(4(1(2(3(x1))))) -> #0(0(2(x1))) #44: #0(4(1(2(3(x1))))) -> #0(2(x1)) #45: #0(1(5(1(x1)))) -> #0(0(2(1(1(5(x1)))))) #46: #0(1(5(1(x1)))) -> #0(2(1(1(5(x1))))) #47: #0(1(5(1(x1)))) -> #5(x1) #48: #0(4(1(2(3(x1))))) -> #0(3(2(4(5(1(x1)))))) #49: #0(4(1(2(3(x1))))) -> #3(2(4(5(1(x1))))) #50: #0(4(1(2(3(x1))))) -> #5(1(x1)) #51: #0(1(2(0(1(x1))))) -> #0(3(0(2(1(1(x1)))))) #52: #0(1(2(0(1(x1))))) -> #3(0(2(1(1(x1))))) #53: #0(1(2(0(1(x1))))) -> #0(2(1(1(x1)))) #54: #3(5(4(1(x1)))) -> #3(4(5(x1))) #55: #3(5(4(1(x1)))) -> #5(x1) #56: #3(5(1(x1))) -> #5(3(1(x1))) #57: #3(5(1(x1))) -> #3(1(x1)) #58: #3(2(4(1(3(x1))))) -> #3(4(3(1(2(x1))))) #59: #3(2(4(1(3(x1))))) -> #3(1(2(x1))) #60: #0(1(2(3(x1)))) -> #3(1(5(0(2(x1))))) #61: #0(1(2(3(x1)))) -> #5(0(2(x1))) #62: #0(1(2(3(x1)))) -> #0(2(x1)) #63: #0(5(1(0(1(x1))))) -> #0(1(5(5(0(1(x1)))))) #64: #0(5(1(0(1(x1))))) -> #5(5(0(1(x1)))) #65: #0(5(1(0(1(x1))))) -> #5(0(1(x1))) #66: #3(0(1(x1))) -> #3(0(0(2(4(x1))))) #67: #3(0(1(x1))) -> #0(0(2(4(x1)))) #68: #3(0(1(x1))) -> #0(2(4(x1))) #69: #5(2(4(2(3(x1))))) -> #3(2(4(5(3(2(x1)))))) #70: #5(2(4(2(3(x1))))) -> #5(3(2(x1))) #71: #5(2(4(2(3(x1))))) -> #3(2(x1)) #72: #0(3(4(2(3(x1))))) -> #0(5(3(4(3(2(x1)))))) #73: #0(3(4(2(3(x1))))) -> #5(3(4(3(2(x1))))) #74: #0(3(4(2(3(x1))))) -> #3(4(3(2(x1)))) #75: #0(3(4(2(3(x1))))) -> #3(2(x1)) #76: #5(2(0(1(x1)))) -> #5(3(1(0(2(4(x1)))))) #77: #5(2(0(1(x1)))) -> #3(1(0(2(4(x1))))) #78: #5(2(0(1(x1)))) -> #0(2(4(x1))) #79: #0(5(3(2(1(x1))))) -> #0(0(2(5(3(1(x1)))))) #80: #0(5(3(2(1(x1))))) -> #0(2(5(3(1(x1))))) #81: #0(5(3(2(1(x1))))) -> #5(3(1(x1))) #82: #0(5(3(2(1(x1))))) -> #3(1(x1)) #83: #0(3(0(5(1(x1))))) -> #0(3(4(5(0(1(x1)))))) #84: #0(3(0(5(1(x1))))) -> #3(4(5(0(1(x1))))) #85: #0(3(0(5(1(x1))))) -> #5(0(1(x1))) #86: #0(3(0(5(1(x1))))) -> #0(1(x1)) #87: #3(5(1(1(x1)))) -> #3(4(5(1(x1)))) #88: #3(5(1(1(x1)))) -> #5(1(x1)) #89: #0(4(5(5(1(x1))))) -> #5(5(0(1(x1)))) #90: #0(4(5(5(1(x1))))) -> #5(0(1(x1))) #91: #0(4(5(5(1(x1))))) -> #0(1(x1)) #92: #3(5(1(3(x1)))) -> #3(5(3(1(2(x1))))) #93: #3(5(1(3(x1)))) -> #5(3(1(2(x1)))) #94: #3(5(1(3(x1)))) -> #3(1(2(x1))) #95: #0(1(2(2(1(x1))))) -> #0(2(1(2(1(3(x1)))))) #96: #0(1(2(2(1(x1))))) -> #3(x1) #97: #3(0(1(2(3(x1))))) -> #3(3(0(2(x1)))) #98: #3(0(1(2(3(x1))))) -> #3(0(2(x1))) #99: #3(0(1(2(3(x1))))) -> #0(2(x1)) #100: #5(1(2(3(x1)))) -> #5(5(3(1(2(x1))))) #101: #5(1(2(3(x1)))) -> #5(3(1(2(x1)))) #102: #5(1(2(3(x1)))) -> #3(1(2(x1))) #103: #3(2(0(1(x1)))) -> #3(0(2(4(5(x1))))) #104: #3(2(0(1(x1)))) -> #0(2(4(5(x1)))) #105: #3(2(0(1(x1)))) -> #5(x1) #106: #0(1(1(x1))) -> #0(2(1(2(1(x1))))) #107: #0(1(1(x1))) -> #0(2(1(1(x1)))) #108: #5(1(3(x1))) -> #5(3(1(2(x1)))) #109: #5(1(3(x1))) -> #3(1(2(x1))) #110: #0(4(5(1(x1)))) -> #0(1(3(4(5(x1))))) #111: #0(4(5(1(x1)))) -> #3(4(5(x1))) #112: #0(4(5(1(x1)))) -> #5(x1) #113: #0(1(1(x1))) -> #0(2(1(x1))) #114: #3(5(1(1(x1)))) -> #5(3(1(2(x1)))) #115: #3(5(1(1(x1)))) -> #3(1(2(x1))) Number of SCCs: 1, DPs: 5 SCC { #34 #35 #38 #71 #105 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. #0 w: [0;0] 1 w: [0,1;0,1] * x1 + [27262;0] 4 w: [0,1;0,1] * x1 + [27262;0] 5 w: [0,1;0,1] * x1 + [27262;0] 3 w: [0,1;0,1] * x1 + [27262;0] 0 w: [1,0;1,0] * x1 #3 w: [1,0;0,0] * x1 + [0;6] #5 w: [0,1;0,0] * x1 + [27261;6] 2 w: [0,1;0,1] * x1 USABLE RULES: { 1..45 } Removed DPs: #34 #35 #71 #105 Number of SCCs: 1, DPs: 1 SCC { #38 } POLO(Sum)... succeeded. #0 w: 0 1 w: 31996 4 w: x1 + 1 5 w: 41366 3 w: x1 + 4684 0 w: 13214 #3 w: 1 #5 w: x1 2 w: 36682 USABLE RULES: { 8 16 21..24 39 44 45 } Removed DPs: #38 Number of SCCs: 0, DPs: 0