YES Input TRS: 1: 0(1(1(2(x1)))) -> 1(3(0(1(2(x1))))) 2: 0(1(1(2(x1)))) -> 1(3(1(0(2(x1))))) 3: 0(1(1(2(x1)))) -> 2(3(1(3(0(1(x1)))))) 4: 0(1(2(0(x1)))) -> 1(0(0(2(2(x1))))) 5: 0(1(2(4(x1)))) -> 0(2(3(4(1(x1))))) 6: 0(1(2(4(x1)))) -> 1(0(4(2(3(x1))))) 7: 0(1(2(4(x1)))) -> 1(2(3(0(4(x1))))) 8: 0(1(2(4(x1)))) -> 2(1(4(0(3(x1))))) 9: 0(1(2(4(x1)))) -> 1(2(3(4(0(5(x1)))))) 10: 0(1(2(4(x1)))) -> 2(1(1(0(3(4(x1)))))) 11: 0(1(2(4(x1)))) -> 4(1(2(2(3(0(x1)))))) 12: 0(1(2(4(x1)))) -> 4(5(0(2(3(1(x1)))))) 13: 0(4(2(0(x1)))) -> 0(4(2(3(0(x1))))) 14: 0(4(2(0(x1)))) -> 2(3(0(4(0(0(x1)))))) 15: 0(4(2(0(x1)))) -> 3(4(0(2(3(0(x1)))))) 16: 0(4(2(0(x1)))) -> 4(2(3(0(4(0(x1)))))) 17: 0(4(2(0(x1)))) -> 4(3(0(0(5(2(x1)))))) 18: 0(4(2(4(x1)))) -> 4(0(2(3(1(4(x1)))))) 19: 0(4(2(4(x1)))) -> 4(0(4(2(0(3(x1)))))) 20: 5(1(2(0(x1)))) -> 2(1(3(5(0(x1))))) 21: 5(1(2(0(x1)))) -> 3(1(0(2(5(x1))))) 22: 5(1(2(0(x1)))) -> 2(3(0(0(1(5(x1)))))) 23: 5(1(2(4(x1)))) -> 3(2(5(1(4(x1))))) 24: 5(1(2(4(x1)))) -> 5(2(1(3(4(x1))))) 25: 5(1(2(4(x1)))) -> 5(5(2(1(4(x1))))) 26: 5(1(2(4(x1)))) -> 0(3(4(5(2(1(x1)))))) 27: 5(1(4(2(x1)))) -> 3(4(5(2(1(x1))))) 28: 5(1(4(2(x1)))) -> 2(1(3(4(5(4(x1)))))) 29: 5(1(4(2(x1)))) -> 3(3(4(2(1(5(x1)))))) 30: 5(4(1(4(x1)))) -> 3(4(4(1(5(4(x1)))))) 31: 5(4(1(4(x1)))) -> 4(1(3(5(0(4(x1)))))) 32: 5(4(1(4(x1)))) -> 5(1(3(4(5(4(x1)))))) 33: 5(4(1(4(x1)))) -> 5(1(5(3(4(4(x1)))))) 34: 5(4(2(0(x1)))) -> 5(4(2(3(0(x1))))) 35: 5(4(2(0(x1)))) -> 0(1(2(3(4(5(x1)))))) 36: 5(4(2(0(x1)))) -> 4(5(3(3(0(2(x1)))))) 37: 0(1(2(0(4(x1))))) -> 0(2(4(1(3(0(x1)))))) 38: 0(1(2(0(4(x1))))) -> 2(0(3(4(0(1(x1)))))) 39: 0(1(2(0(4(x1))))) -> 4(0(2(3(1(0(x1)))))) 40: 0(1(4(2(2(x1))))) -> 1(2(3(4(0(2(x1)))))) 41: 5(0(1(2(4(x1))))) -> 3(0(2(1(4(5(x1)))))) 42: 5(1(2(2(4(x1))))) -> 5(2(2(1(4(5(x1)))))) 43: 5(1(2(4(0(x1))))) -> 5(0(2(1(3(4(x1)))))) 44: 5(1(2(4(0(x1))))) -> 5(0(3(2(1(4(x1)))))) 45: 5(1(3(1(4(x1))))) -> 1(5(1(3(4(0(x1)))))) 46: 5(1(4(1(2(x1))))) -> 2(1(5(3(4(1(x1)))))) 47: 5(4(1(1(4(x1))))) -> 1(1(3(4(5(4(x1)))))) 48: 5(4(1(4(0(x1))))) -> 3(4(0(4(5(1(x1)))))) 49: 5(4(3(2(0(x1))))) -> 5(4(0(3(2(3(x1)))))) 50: 5(4(5(2(0(x1))))) -> 5(0(5(4(4(2(x1)))))) Number of strict rules: 50 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #0(1(1(2(x1)))) -> #0(2(x1)) #2: #5(1(2(4(0(x1))))) -> #5(0(2(1(3(4(x1)))))) #3: #5(1(2(4(0(x1))))) -> #0(2(1(3(4(x1))))) #4: #5(1(4(2(x1)))) -> #5(x1) #5: #5(4(2(0(x1)))) -> #0(1(2(3(4(5(x1)))))) #6: #5(4(2(0(x1)))) -> #5(x1) #7: #5(1(4(1(2(x1))))) -> #5(3(4(1(x1)))) #8: #5(1(2(2(4(x1))))) -> #5(2(2(1(4(5(x1)))))) #9: #5(1(2(2(4(x1))))) -> #5(x1) #10: #5(0(1(2(4(x1))))) -> #0(2(1(4(5(x1))))) #11: #5(0(1(2(4(x1))))) -> #5(x1) #12: #0(1(2(0(4(x1))))) -> #0(2(4(1(3(0(x1)))))) #13: #0(1(2(0(4(x1))))) -> #0(x1) #14: #5(4(1(1(4(x1))))) -> #5(4(x1)) #15: #5(4(1(4(0(x1))))) -> #0(4(5(1(x1)))) #16: #5(4(1(4(0(x1))))) -> #5(1(x1)) #17: #0(1(2(0(4(x1))))) -> #0(3(4(0(1(x1))))) #18: #0(1(2(0(4(x1))))) -> #0(1(x1)) #19: #0(1(2(4(x1)))) -> #0(4(2(3(x1)))) #20: #0(1(4(2(2(x1))))) -> #0(2(x1)) #21: #0(4(2(0(x1)))) -> #0(4(2(3(0(x1))))) #22: #0(1(2(4(x1)))) -> #0(5(x1)) #23: #0(1(2(4(x1)))) -> #5(x1) #24: #0(1(2(4(x1)))) -> #0(x1) #25: #5(1(2(4(x1)))) -> #5(2(1(3(4(x1))))) #26: #5(1(2(4(x1)))) -> #5(1(4(x1))) #27: #5(1(3(1(4(x1))))) -> #5(1(3(4(0(x1))))) #28: #5(1(3(1(4(x1))))) -> #0(x1) #29: #0(1(2(4(x1)))) -> #5(0(2(3(1(x1))))) #30: #0(1(2(4(x1)))) -> #0(2(3(1(x1)))) #31: #5(4(1(4(x1)))) -> #5(0(4(x1))) #32: #5(4(1(4(x1)))) -> #0(4(x1)) #33: #0(4(2(0(x1)))) -> #0(4(0(0(x1)))) #34: #0(4(2(0(x1)))) -> #0(0(x1)) #35: #5(4(1(4(x1)))) -> #5(4(x1)) #36: #5(4(3(2(0(x1))))) -> #5(4(0(3(2(3(x1)))))) #37: #5(4(3(2(0(x1))))) -> #0(3(2(3(x1)))) #38: #5(1(2(4(x1)))) -> #5(5(2(1(4(x1))))) #39: #5(1(2(4(x1)))) -> #5(2(1(4(x1)))) #40: #5(1(2(0(x1)))) -> #5(0(x1)) #41: #0(1(2(4(x1)))) -> #0(4(x1)) #42: #0(1(2(0(4(x1))))) -> #0(2(3(1(0(x1))))) #43: #0(1(2(0(4(x1))))) -> #0(x1) #44: #0(1(2(4(x1)))) -> #0(3(4(x1))) #45: #5(4(1(4(x1)))) -> #5(1(5(3(4(4(x1)))))) #46: #5(4(1(4(x1)))) -> #5(3(4(4(x1)))) #47: #0(1(2(4(x1)))) -> #0(2(3(4(1(x1))))) #48: #5(1(2(4(0(x1))))) -> #5(0(3(2(1(4(x1)))))) #49: #5(1(2(4(0(x1))))) -> #0(3(2(1(4(x1))))) #50: #5(1(4(2(x1)))) -> #5(4(x1)) #51: #5(1(2(0(x1)))) -> #0(0(1(5(x1)))) #52: #5(1(2(0(x1)))) -> #0(1(5(x1))) #53: #5(1(2(0(x1)))) -> #5(x1) #54: #5(4(2(0(x1)))) -> #5(4(2(3(0(x1))))) #55: #5(1(4(2(x1)))) -> #5(2(1(x1))) #56: #0(4(2(0(x1)))) -> #0(0(5(2(x1)))) #57: #0(4(2(0(x1)))) -> #0(5(2(x1))) #58: #0(4(2(0(x1)))) -> #5(2(x1)) #59: #5(4(1(4(x1)))) -> #5(1(3(4(5(4(x1)))))) #60: #5(4(1(4(x1)))) -> #5(4(x1)) #61: #0(4(2(4(x1)))) -> #0(4(2(0(3(x1))))) #62: #0(4(2(4(x1)))) -> #0(3(x1)) #63: #5(1(2(4(x1)))) -> #0(3(4(5(2(1(x1)))))) #64: #5(1(2(4(x1)))) -> #5(2(1(x1))) #65: #5(4(2(0(x1)))) -> #5(3(3(0(2(x1))))) #66: #5(4(2(0(x1)))) -> #0(2(x1)) #67: #5(1(2(0(x1)))) -> #0(2(5(x1))) #68: #5(1(2(0(x1)))) -> #5(x1) #69: #0(4(2(0(x1)))) -> #0(4(0(x1))) #70: #0(1(1(2(x1)))) -> #0(1(x1)) #71: #0(1(1(2(x1)))) -> #0(1(2(x1))) #72: #0(1(2(4(x1)))) -> #0(3(x1)) #73: #0(4(2(0(x1)))) -> #0(2(3(0(x1)))) #74: #0(1(2(0(x1)))) -> #0(0(2(2(x1)))) #75: #0(1(2(0(x1)))) -> #0(2(2(x1))) #76: #5(4(5(2(0(x1))))) -> #5(0(5(4(4(2(x1)))))) #77: #5(4(5(2(0(x1))))) -> #0(5(4(4(2(x1))))) #78: #5(4(5(2(0(x1))))) -> #5(4(4(2(x1)))) #79: #0(4(2(4(x1)))) -> #0(2(3(1(4(x1))))) Number of SCCs: 2, DPs: 22 SCC { #69 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. #0 w: max(x1 - 1, 0) 1 w: 41656 4 w: max(x1 - 41655, 0) 5 w: 104135 3 w: max(x1 - 62482, 0) 0 w: max(x1 + 41654, 0) #5 w: max(x1 - 1, 0) 2 w: max(x1 + 41653, 0) USABLE RULES: { 1..50 } Removed DPs: #69 Number of SCCs: 1, DPs: 21 SCC { #4 #6 #9 #11 #13 #14 #16 #18 #23 #24 #26 #28 #35 #40 #43 #50 #53 #60 #68 #70 #71 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. #0 w: [0,1;0,0] * x1 + [1;0] 1 w: [0,0;0,1] * x1 + [0;1] 4 w: [0,0;0,1] * x1 + [1;0] 5 w: [0,0;0,1] * x1 + [1;0] 3 w: [0,0;0,1] * x1 0 w: x1 + [1;0] #5 w: [0,1;0,0] * x1 2 w: [0,0;1,1] * x1 + [0;1] USABLE RULES: { 1..50 } Removed DPs: #4 #6 #9 #11 #13 #14 #18 #23 #24 #26 #28 #35 #40 #43 #50 #53 #60 #68 #70 #71 Number of SCCs: 0, DPs: 0