YES Input TRS: 1: 0(0(0(x1))) -> 0(0(1(0(2(x1))))) 2: 0(3(2(x1))) -> 4(3(0(2(x1)))) 3: 0(0(4(2(x1)))) -> 0(4(1(0(2(x1))))) 4: 0(0(5(2(x1)))) -> 5(0(2(3(0(x1))))) 5: 0(1(3(2(x1)))) -> 0(3(1(0(2(x1))))) 6: 0(1(3(2(x1)))) -> 3(1(1(0(2(x1))))) 7: 0(1(3(2(x1)))) -> 0(1(4(3(1(2(x1)))))) 8: 0(4(1(3(x1)))) -> 1(4(3(0(2(2(x1)))))) 9: 0(4(2(3(x1)))) -> 5(4(3(0(2(x1))))) 10: 0(4(5(2(x1)))) -> 5(0(2(2(4(2(x1)))))) 11: 0(5(1(3(x1)))) -> 3(0(1(5(1(2(x1)))))) 12: 0(5(3(0(x1)))) -> 5(0(1(4(3(0(x1)))))) 13: 0(5(3(2(x1)))) -> 5(1(5(0(2(3(x1)))))) 14: 4(0(2(3(x1)))) -> 3(4(3(0(2(x1))))) 15: 4(0(2(3(x1)))) -> 4(3(5(0(2(x1))))) 16: 4(4(1(3(x1)))) -> 4(3(4(1(2(2(x1)))))) 17: 4(5(2(0(x1)))) -> 4(2(1(5(0(2(x1)))))) 18: 4(5(2(0(x1)))) -> 5(1(0(2(2(4(x1)))))) 19: 5(1(0(0(x1)))) -> 5(1(0(2(0(x1))))) 20: 5(1(0(0(x1)))) -> 5(2(1(0(2(0(x1)))))) 21: 5(1(3(0(x1)))) -> 5(0(2(1(3(x1))))) 22: 5(1(3(2(x1)))) -> 3(0(1(5(1(2(x1)))))) 23: 5(1(3(2(x1)))) -> 3(1(1(5(2(2(x1)))))) 24: 5(3(0(0(x1)))) -> 5(0(4(3(0(2(x1)))))) 25: 0(0(4(1(3(x1))))) -> 4(0(1(0(2(3(x1)))))) 26: 0(0(4(5(2(x1))))) -> 5(0(1(0(2(4(x1)))))) 27: 0(0(5(3(2(x1))))) -> 0(1(5(0(2(3(x1)))))) 28: 0(1(0(5(2(x1))))) -> 1(0(2(5(1(0(x1)))))) 29: 0(1(4(5(2(x1))))) -> 2(1(5(0(2(4(x1)))))) 30: 0(3(1(4(0(x1))))) -> 4(1(0(1(0(3(x1)))))) 31: 0(3(2(0(0(x1))))) -> 0(0(1(0(2(3(x1)))))) 32: 0(3(4(0(2(x1))))) -> 4(3(0(2(1(0(x1)))))) 33: 0(3(4(0(2(x1))))) -> 4(3(0(2(3(0(x1)))))) 34: 0(3(4(4(2(x1))))) -> 4(0(3(4(2(2(x1)))))) 35: 0(4(2(5(3(x1))))) -> 0(4(3(5(1(2(x1)))))) 36: 0(5(1(2(0(x1))))) -> 3(0(1(5(0(2(x1)))))) 37: 4(4(2(2(0(x1))))) -> 4(1(0(2(2(4(x1)))))) 38: 4(5(1(2(0(x1))))) -> 5(0(4(1(2(2(x1)))))) 39: 4(5(2(3(2(x1))))) -> 5(4(3(5(2(2(x1)))))) 40: 5(1(0(3(2(x1))))) -> 5(0(3(1(0(2(x1)))))) 41: 5(1(0(5(3(x1))))) -> 5(5(0(1(3(1(x1)))))) 42: 5(1(3(0(0(x1))))) -> 3(5(0(1(2(0(x1)))))) 43: 5(1(3(0(2(x1))))) -> 3(0(2(1(5(2(x1)))))) 44: 5(1(3(0(2(x1))))) -> 5(0(1(0(3(2(x1)))))) 45: 5(1(3(0(2(x1))))) -> 5(0(1(1(2(3(x1)))))) 46: 5(1(3(2(0(x1))))) -> 5(3(1(5(2(0(x1)))))) 47: 5(1(3(2(3(x1))))) -> 3(4(3(5(1(2(x1)))))) 48: 5(1(4(5(2(x1))))) -> 5(1(4(1(5(2(x1)))))) 49: 5(5(1(3(2(x1))))) -> 3(5(5(4(1(2(x1)))))) Number of strict rules: 49 Direct POLO(bPol) ... failed. Uncurrying 5 1: 0(0(0(x1))) -> 0(0(1(0(2(x1))))) 2: 0(3(2(x1))) -> 4(3(0(2(x1)))) 3: 0(0(4(2(x1)))) -> 0(4(1(0(2(x1))))) 4: 0(0(5^1_2(x1))) -> 5(0(2(3(0(x1))))) 5: 0(1(3(2(x1)))) -> 0(3(1(0(2(x1))))) 6: 0(1(3(2(x1)))) -> 3(1(1(0(2(x1))))) 7: 0(1(3(2(x1)))) -> 0(1(4(3(1(2(x1)))))) 8: 0(4(1(3(x1)))) -> 1(4(3(0(2(2(x1)))))) 9: 0(4(2(3(x1)))) -> 5(4(3(0(2(x1))))) 10: 0(4(5^1_2(x1))) -> 5(0(2(2(4(2(x1)))))) 11: 0(5^1_1(3(x1))) -> 3(0(1(5^1_1(2(x1))))) 12: 0(5^1_3(0(x1))) -> 5(0(1(4(3(0(x1)))))) 13: 0(5^1_3(2(x1))) -> 5^1_1(5(0(2(3(x1))))) 14: 4(0(2(3(x1)))) -> 3(4(3(0(2(x1))))) 15: 4(0(2(3(x1)))) -> 4(3(5(0(2(x1))))) 16: 4(4(1(3(x1)))) -> 4(3(4(1(2(2(x1)))))) 17: 4(5^1_2(0(x1))) -> 4(2(1(5(0(2(x1)))))) 18: 4(5^1_2(0(x1))) -> 5^1_1(0(2(2(4(x1))))) 19: 5^1_1(0(0(x1))) -> 5^1_1(0(2(0(x1)))) 20: 5^1_1(0(0(x1))) -> 5^1_2(1(0(2(0(x1))))) 21: 5^1_1(3(0(x1))) -> 5(0(2(1(3(x1))))) 22: 5^1_1(3(2(x1))) -> 3(0(1(5^1_1(2(x1))))) 23: 5^1_1(3(2(x1))) -> 3(1(1(5^1_2(2(x1))))) 24: 5^1_3(0(0(x1))) -> 5(0(4(3(0(2(x1)))))) 25: 0(0(4(1(3(x1))))) -> 4(0(1(0(2(3(x1)))))) 26: 0(0(4(5^1_2(x1)))) -> 5(0(1(0(2(4(x1)))))) 27: 0(0(5^1_3(2(x1)))) -> 0(1(5(0(2(3(x1)))))) 28: 0(1(0(5^1_2(x1)))) -> 1(0(2(5^1_1(0(x1))))) 29: 0(1(4(5^1_2(x1)))) -> 2(1(5(0(2(4(x1)))))) 30: 0(3(1(4(0(x1))))) -> 4(1(0(1(0(3(x1)))))) 31: 0(3(2(0(0(x1))))) -> 0(0(1(0(2(3(x1)))))) 32: 0(3(4(0(2(x1))))) -> 4(3(0(2(1(0(x1)))))) 33: 0(3(4(0(2(x1))))) -> 4(3(0(2(3(0(x1)))))) 34: 0(3(4(4(2(x1))))) -> 4(0(3(4(2(2(x1)))))) 35: 0(4(2(5^1_3(x1)))) -> 0(4(3(5^1_1(2(x1))))) 36: 0(5^1_1(2(0(x1)))) -> 3(0(1(5(0(2(x1)))))) 37: 4(4(2(2(0(x1))))) -> 4(1(0(2(2(4(x1)))))) 38: 4(5^1_1(2(0(x1)))) -> 5(0(4(1(2(2(x1)))))) 39: 4(5^1_2(3(2(x1)))) -> 5(4(3(5^1_2(2(x1))))) 40: 5^1_1(0(3(2(x1)))) -> 5(0(3(1(0(2(x1)))))) 41: 5^1_1(0(5^1_3(x1))) -> 5(5(0(1(3(1(x1)))))) 42: 5^1_1(3(0(0(x1)))) -> 3(5(0(1(2(0(x1)))))) 43: 5^1_1(3(0(2(x1)))) -> 3(0(2(1(5^1_2(x1))))) 44: 5^1_1(3(0(2(x1)))) -> 5(0(1(0(3(2(x1)))))) 45: 5^1_1(3(0(2(x1)))) -> 5(0(1(1(2(3(x1)))))) 46: 5^1_1(3(2(0(x1)))) -> 5^1_3(1(5^1_2(0(x1)))) 47: 5^1_1(3(2(3(x1)))) -> 3(4(3(5^1_1(2(x1))))) 48: 5^1_1(4(5^1_2(x1))) -> 5^1_1(4(1(5^1_2(x1)))) 49: 5(5^1_1(3(2(x1)))) -> 3(5(5(4(1(2(x1)))))) 50: 5(2(_1)) ->= 5^1_2(_1) 51: 5(1(_1)) ->= 5^1_1(_1) 52: 5(3(_1)) ->= 5^1_3(_1) Number of strict rules: 49 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #0(3(2(x1))) -> #4(3(0(2(x1)))) #2: #0(3(2(x1))) -> #0(2(x1)) #3: #5^1_1(3(0(2(x1)))) -> #0(2(1(5^1_2(x1)))) #4: #0(1(4(5^1_2(x1)))) -> #5(0(2(4(x1)))) #5: #0(1(4(5^1_2(x1)))) -> #0(2(4(x1))) #6: #0(1(4(5^1_2(x1)))) -> #4(x1) #7: #0(4(2(5^1_3(x1)))) -> #0(4(3(5^1_1(2(x1))))) #8: #0(4(2(5^1_3(x1)))) -> #4(3(5^1_1(2(x1)))) #9: #0(4(2(5^1_3(x1)))) -> #5^1_1(2(x1)) #10: #5^1_1(3(2(0(x1)))) -> #5^1_3(1(5^1_2(0(x1)))) #11: #5^1_1(3(0(0(x1)))) -> #5(0(1(2(0(x1))))) #12: #5^1_1(3(0(0(x1)))) -> #0(1(2(0(x1)))) #13: #5^1_1(0(5^1_3(x1))) -> #5(5(0(1(3(1(x1)))))) #14: #5^1_1(0(5^1_3(x1))) -> #5(0(1(3(1(x1))))) #15: #5^1_1(0(5^1_3(x1))) -> #0(1(3(1(x1)))) #16: #4(4(2(2(0(x1))))) -> #4(1(0(2(2(4(x1)))))) #17: #4(4(2(2(0(x1))))) -> #0(2(2(4(x1)))) #18: #4(4(2(2(0(x1))))) -> #4(x1) #19: #5^1_1(3(2(3(x1)))) -> #4(3(5^1_1(2(x1)))) #20: #5^1_1(3(2(3(x1)))) -> #5^1_1(2(x1)) #21: #5^1_1(4(5^1_2(x1))) -> #5^1_1(4(1(5^1_2(x1)))) #22: #5^1_1(4(5^1_2(x1))) -> #4(1(5^1_2(x1))) #23: #4(5^1_1(2(0(x1)))) -> #5(0(4(1(2(2(x1)))))) #24: #4(5^1_1(2(0(x1)))) -> #0(4(1(2(2(x1))))) #25: #4(5^1_1(2(0(x1)))) -> #4(1(2(2(x1)))) #26: #0(1(3(2(x1)))) -> #0(2(x1)) #27: #5^1_1(0(3(2(x1)))) -> #5(0(3(1(0(2(x1)))))) #28: #5^1_1(0(3(2(x1)))) -> #0(3(1(0(2(x1))))) #29: #5^1_1(0(3(2(x1)))) -> #0(2(x1)) #30: #5(1(_1)) ->? #5^1_1(_1) #31: #0(5^1_3(2(x1))) -> #5^1_1(5(0(2(3(x1))))) #32: #0(5^1_3(2(x1))) -> #5(0(2(3(x1)))) #33: #0(5^1_3(2(x1))) -> #0(2(3(x1))) #34: #0(4(2(3(x1)))) -> #5(4(3(0(2(x1))))) #35: #0(4(2(3(x1)))) -> #4(3(0(2(x1)))) #36: #0(4(2(3(x1)))) -> #0(2(x1)) #37: #0(5^1_1(3(x1))) -> #0(1(5^1_1(2(x1)))) #38: #0(5^1_1(3(x1))) -> #5^1_1(2(x1)) #39: #5^1_3(0(0(x1))) -> #5(0(4(3(0(2(x1)))))) #40: #5^1_3(0(0(x1))) -> #0(4(3(0(2(x1))))) #41: #5^1_3(0(0(x1))) -> #4(3(0(2(x1)))) #42: #5^1_3(0(0(x1))) -> #0(2(x1)) #43: #5^1_1(3(0(2(x1)))) -> #5(0(1(1(2(3(x1)))))) #44: #5^1_1(3(0(2(x1)))) -> #0(1(1(2(3(x1))))) #45: #0(5^1_3(0(x1))) -> #5(0(1(4(3(0(x1)))))) #46: #0(5^1_3(0(x1))) -> #0(1(4(3(0(x1))))) #47: #0(5^1_3(0(x1))) -> #4(3(0(x1))) #48: #0(3(2(0(0(x1))))) -> #0(0(1(0(2(3(x1)))))) #49: #0(3(2(0(0(x1))))) -> #0(1(0(2(3(x1))))) #50: #0(3(2(0(0(x1))))) -> #0(2(3(x1))) #51: #4(0(2(3(x1)))) -> #4(3(0(2(x1)))) #52: #4(0(2(3(x1)))) -> #0(2(x1)) #53: #0(3(1(4(0(x1))))) -> #4(1(0(1(0(3(x1)))))) #54: #0(3(1(4(0(x1))))) -> #0(1(0(3(x1)))) #55: #0(3(1(4(0(x1))))) -> #0(3(x1)) #56: #5(3(_1)) ->? #5^1_3(_1) #57: #5(5^1_1(3(2(x1)))) -> #5(5(4(1(2(x1))))) #58: #5(5^1_1(3(2(x1)))) -> #5(4(1(2(x1)))) #59: #5(5^1_1(3(2(x1)))) -> #4(1(2(x1))) #60: #0(0(4(1(3(x1))))) -> #4(0(1(0(2(3(x1)))))) #61: #0(0(4(1(3(x1))))) -> #0(1(0(2(3(x1))))) #62: #0(0(4(1(3(x1))))) -> #0(2(3(x1))) #63: #5^1_1(0(0(x1))) -> #0(2(0(x1))) #64: #0(1(3(2(x1)))) -> #0(1(4(3(1(2(x1)))))) #65: #0(1(3(2(x1)))) -> #4(3(1(2(x1)))) #66: #4(5^1_2(3(2(x1)))) -> #5(4(3(5^1_2(2(x1))))) #67: #4(5^1_2(3(2(x1)))) -> #4(3(5^1_2(2(x1)))) #68: #0(4(5^1_2(x1))) -> #5(0(2(2(4(2(x1)))))) #69: #0(4(5^1_2(x1))) -> #0(2(2(4(2(x1))))) #70: #0(4(5^1_2(x1))) -> #4(2(x1)) #71: #0(3(4(0(2(x1))))) -> #4(3(0(2(3(0(x1)))))) #72: #0(3(4(0(2(x1))))) -> #0(2(3(0(x1)))) #73: #0(3(4(0(2(x1))))) -> #0(x1) #74: #0(1(3(2(x1)))) -> #0(3(1(0(2(x1))))) #75: #0(1(3(2(x1)))) -> #0(2(x1)) #76: #5^1_1(3(0(2(x1)))) -> #5(0(1(0(3(2(x1)))))) #77: #5^1_1(3(0(2(x1)))) -> #0(1(0(3(2(x1))))) #78: #5^1_1(3(0(2(x1)))) -> #0(3(2(x1))) #79: #0(1(0(5^1_2(x1)))) -> #0(2(5^1_1(0(x1)))) #80: #0(1(0(5^1_2(x1)))) -> #5^1_1(0(x1)) #81: #0(1(0(5^1_2(x1)))) -> #0(x1) #82: #5^1_1(3(2(x1))) -> #0(1(5^1_1(2(x1)))) #83: #5^1_1(3(2(x1))) -> #5^1_1(2(x1)) #84: #0(3(4(4(2(x1))))) -> #4(0(3(4(2(2(x1)))))) #85: #0(3(4(4(2(x1))))) -> #0(3(4(2(2(x1))))) #86: #0(3(4(4(2(x1))))) -> #4(2(2(x1))) #87: #0(0(5^1_3(2(x1)))) -> #0(1(5(0(2(3(x1)))))) #88: #0(0(5^1_3(2(x1)))) -> #5(0(2(3(x1)))) #89: #0(0(5^1_3(2(x1)))) -> #0(2(3(x1))) #90: #4(5^1_2(0(x1))) -> #4(2(1(5(0(2(x1)))))) #91: #4(5^1_2(0(x1))) -> #5(0(2(x1))) #92: #4(5^1_2(0(x1))) -> #0(2(x1)) #93: #5^1_1(0(0(x1))) -> #5^1_1(0(2(0(x1)))) #94: #5^1_1(0(0(x1))) -> #0(2(0(x1))) #95: #0(3(4(0(2(x1))))) -> #4(3(0(2(1(0(x1)))))) #96: #0(3(4(0(2(x1))))) -> #0(2(1(0(x1)))) #97: #0(3(4(0(2(x1))))) -> #0(x1) #98: #0(0(4(5^1_2(x1)))) -> #5(0(1(0(2(4(x1)))))) #99: #0(0(4(5^1_2(x1)))) -> #0(1(0(2(4(x1))))) #100: #0(0(4(5^1_2(x1)))) -> #0(2(4(x1))) #101: #0(0(4(5^1_2(x1)))) -> #4(x1) #102: #0(5^1_1(2(0(x1)))) -> #0(1(5(0(2(x1))))) #103: #0(5^1_1(2(0(x1)))) -> #5(0(2(x1))) #104: #0(5^1_1(2(0(x1)))) -> #0(2(x1)) #105: #5^1_1(3(0(x1))) -> #5(0(2(1(3(x1))))) #106: #5^1_1(3(0(x1))) -> #0(2(1(3(x1)))) #107: #4(4(1(3(x1)))) -> #4(3(4(1(2(2(x1)))))) #108: #4(4(1(3(x1)))) -> #4(1(2(2(x1)))) #109: #0(0(4(2(x1)))) -> #0(4(1(0(2(x1))))) #110: #0(0(4(2(x1)))) -> #4(1(0(2(x1)))) #111: #0(0(4(2(x1)))) -> #0(2(x1)) #112: #0(0(0(x1))) -> #0(0(1(0(2(x1))))) #113: #0(0(0(x1))) -> #0(1(0(2(x1)))) #114: #0(0(0(x1))) -> #0(2(x1)) #115: #0(4(1(3(x1)))) -> #4(3(0(2(2(x1))))) #116: #0(4(1(3(x1)))) -> #0(2(2(x1))) #117: #4(0(2(3(x1)))) -> #4(3(5(0(2(x1))))) #118: #4(0(2(3(x1)))) -> #5(0(2(x1))) #119: #4(0(2(3(x1)))) -> #0(2(x1)) #120: #0(0(5^1_2(x1))) -> #5(0(2(3(0(x1))))) #121: #0(0(5^1_2(x1))) -> #0(2(3(0(x1)))) #122: #0(0(5^1_2(x1))) -> #0(x1) #123: #4(5^1_2(0(x1))) -> #5^1_1(0(2(2(4(x1))))) #124: #4(5^1_2(0(x1))) -> #0(2(2(4(x1)))) #125: #4(5^1_2(0(x1))) -> #4(x1) Number of SCCs: 2, DPs: 7 SCC { #18 #125 } POLO(Sum)... succeeded. 5^1_2 w: x1 #0 w: 0 1 w: 0 5^1_1 w: 0 4 w: x1 #5^1_1 w: 0 5^1_3 w: 0 5 w: 0 3 w: 0 #4 w: x1 0 w: x1 + 1 #5^1_3 w: 0 #5 w: 0 2 w: x1 USABLE RULES: { } Removed DPs: #18 #125 Number of SCCs: 1, DPs: 5 SCC { #55 #73 #81 #97 #122 } POLO(Sum)... succeeded. 5^1_2 w: x1 + 8366 #0 w: x1 1 w: x1 5^1_1 w: 0 4 w: x1 #5^1_1 w: 0 5^1_3 w: 0 5 w: 0 3 w: x1 + 33036 #4 w: 0 0 w: x1 + 1 #5^1_3 w: 0 #5 w: 0 2 w: x1 + 11293 USABLE RULES: { } Removed DPs: #55 #73 #81 #97 #122 Number of SCCs: 0, DPs: 0