YES Input TRS: 1: 3(1(x1)) -> 4(1(x1)) 2: 5(9(x1)) -> 2(6(5(x1))) 3: 3(5(x1)) -> 8(9(7(x1))) 4: 9(x1) -> 3(2(3(x1))) 5: 8(4(x1)) -> 6(x1) 6: 2(6(x1)) -> 4(3(x1)) 7: 3(8(x1)) -> 3(2(7(x1))) 8: 9(x1) -> 5(0(2(x1))) 9: 8(8(4(x1))) -> 1(9(x1)) 10: 7(1(x1)) -> 6(9(x1)) 11: 3(9(x1)) -> 9(3(x1)) 12: 7(5(x1)) -> 1(0(x1)) Number of strict rules: 12 Direct POLO(bPol) ... failed. Uncurrying 2 1: 3(1(x1)) -> 4(1(x1)) 2: 5(9(x1)) -> 2^1_6(5(x1)) 3: 3(5(x1)) -> 8(9(7(x1))) 4: 9(x1) -> 3(2(3(x1))) 5: 8(4(x1)) -> 6(x1) 6: 2^1_6(x1) -> 4(3(x1)) 7: 3(8(x1)) -> 3(2(7(x1))) 8: 9(x1) -> 5(0(2(x1))) 9: 8(8(4(x1))) -> 1(9(x1)) 10: 7(1(x1)) -> 6(9(x1)) 11: 3(9(x1)) -> 9(3(x1)) 12: 7(5(x1)) -> 1(0(x1)) 13: 2(6(_1)) ->= 2^1_6(_1) Number of strict rules: 12 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #5(9(x1)) -> #2^1_6(5(x1)) #2: #5(9(x1)) -> #5(x1) #3: #2^1_6(x1) -> #3(x1) #4: #2(6(_1)) ->? #2^1_6(_1) #5: #8(8(4(x1))) -> #9(x1) #6: #3(9(x1)) -> #9(3(x1)) #7: #3(9(x1)) -> #3(x1) #8: #3(8(x1)) -> #3(2(7(x1))) #9: #3(8(x1)) -> #2(7(x1)) #10: #3(8(x1)) -> #7(x1) #11: #7(1(x1)) -> #9(x1) #12: #3(5(x1)) -> #8(9(7(x1))) #13: #3(5(x1)) -> #9(7(x1)) #14: #3(5(x1)) -> #7(x1) #15: #9(x1) -> #5(0(2(x1))) #16: #9(x1) -> #2(x1) #17: #9(x1) -> #3(2(3(x1))) #18: #9(x1) -> #2(3(x1)) #19: #9(x1) -> #3(x1) Number of SCCs: 2, DPs: 12 SCC { #2 } POLO(Sum)... succeeded. 7 w: 0 1 w: 0 2^1_6 w: 0 4 w: 0 #7 w: 0 5 w: 0 3 w: 0 #8 w: 0 #2 w: 0 9 w: x1 + 1 8 w: 0 #9 w: 0 0 w: 0 #3 w: 0 #2^1_6 w: 0 #5 w: x1 2 w: 0 6 w: 0 USABLE RULES: { } Removed DPs: #2 Number of SCCs: 1, DPs: 11 SCC { #3 #4 #6 #7 #9..11 #13 #14 #16 #19 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. 7 w: [0,1;0,0] * x1 + [0;19393] 1 w: [0,0;1,0] * x1 + [0;19392] 2^1_6 w: [0;19392] 4 w: [0,0;1,0] * x1 + [0;19392] #7 w: [0,1;0,1] * x1 5 w: [0,1;0,1] * x1 3 w: [0,0;1,1] * x1 #8 w: [0;0] #2 w: [1,0;1,0] * x1 9 w: [1,0;0,0] * x1 8 w: [0,1;1,0] * x1 #9 w: [1,0;1,0] * x1 + [1;0] 0 w: [1;0] #3 w: [1,0;1,0] * x1 + [1;0] #2^1_6 w: [1,0;1,0] * x1 + [2;0] #5 w: [0;0] 2 w: [0,0;1,0] * x1 6 w: [1,0;0,0] * x1 + [19392;0] USABLE RULES: { 1 3..13 } Removed DPs: #3 #4 #9..11 #14 #16 Number of SCCs: 1, DPs: 4 SCC { #6 #7 #13 #19 } POLO(Sum)... succeeded. 7 w: 1 1 w: 0 2^1_6 w: 1 4 w: 1 #7 w: 0 5 w: x1 + 31894 3 w: x1 + 1 #8 w: 0 #2 w: 0 9 w: x1 + 31894 8 w: 21657 #9 w: x1 + 31892 0 w: 0 #3 w: x1 #2^1_6 w: 0 #5 w: 0 2 w: x1 + 21656 6 w: 1 USABLE RULES: { 1 3..13 } Removed DPs: #6 #7 #13 #19 Number of SCCs: 0, DPs: 0