Input TRS: 1: c(c(c(b(x)))) -> a(1(),b(c(x))) 2: b(c(b(c(x)))) -> a(0(),a(1(),x)) 3: a(0(),x) -> c(c(x)) 4: a(1(),x) -> c(b(x)) Number of strict rules: 4 Direct Order(PosReal,>,Poly) ... failed. Freezing a 1: c(c(c(b(x)))) -> a❆1_1(b(c(x))) 2: b(c(b(c(x)))) -> a❆1_0(a❆1_1(x)) 3: a❆1_0(x) -> c(c(x)) 4: a❆1_1(x) -> c(b(x)) 5: a(1(),_1) ->= a❆1_1(_1) 6: a(0(),_1) ->= a❆1_0(_1) Number of strict rules: 4 Direct Order(PosReal,>,Poly) ... removes: 5 6 a(x1,x2) weight: (/ 84955 2) + x1 + x2 1() weight: 0 b(x1) weight: (/ 42477 2) + x1 a❆1_0(x1) weight: 42477 + x1 c(x1) weight: (/ 42477 2) + x1 0() weight: 0 a❆1_1(x1) weight: 42477 + x1 Number of strict rules: 4 Direct Order(PosReal,>,Poly) ... failed. Dependency Pairs: #1: #b(c(b(c(x)))) -> #a❆1_0(a❆1_1(x)) #2: #b(c(b(c(x)))) -> #a❆1_1(x) #3: #a❆1_0(x) -> #c(c(x)) #4: #a❆1_0(x) -> #c(x) #5: #c(c(c(b(x)))) -> #a❆1_1(b(c(x))) #6: #c(c(c(b(x)))) -> #b(c(x)) #7: #c(c(c(b(x)))) -> #c(x) #8: #a❆1_1(x) -> #c(b(x)) #9: #a❆1_1(x) -> #b(x) Number of SCCs: 1, DPs: 9, edges: 22 SCC { #1..9 } Removing DPs: Order(PosReal,>,Sum)... succeeded. a(x1,x2) weight: 0 1() weight: 0 #a❆1_1(x1) weight: (/ 3 8) + x1 b(x1) weight: (/ 3 8) + x1 a❆1_0(x1) weight: (/ 3 4) + x1 c(x1) weight: (/ 3 8) + x1 0() weight: 0 #a❆1_0(x1) weight: (/ 1 2) + x1 #c(x1) weight: x1 a❆1_1(x1) weight: (/ 3 4) + x1 #b(x1) weight: (/ 1 4) + x1 Usable rules: { 1..4 } Removed DPs: #1..4 #6 #7 #9 Number of SCCs: 1, DPs: 2, edges: 2 SCC { #5 #8 } Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... Order(PosReal,>,MaxSum-Sum; NegReal,≥,Sum)... failed. Removing edges: failed. Finding a loop... failed. MAYBE