Input TRS: 1: f(true(),x) -> f(gt(x,0()),double(x)) 2: gt(s(x),0()) -> true() 3: gt(0(),y) -> false() 4: gt(s(x),s(y)) -> gt(x,y) 5: double(x) -> doubleAkk(x,0()) 6: doubleAkk(0(),y) -> y 7: doubleAkk(s(x),y) -> doubleAkk(x,s(s(y))) Number of strict rules: 7 Direct Order(PosReal,>,Poly) ... failed. Freezing ... failed. Dependency Pairs: #1: #doubleAkk(s(x),y) -> #doubleAkk(x,s(s(y))) #2: #double(x) -> #doubleAkk(x,0()) #3: #f(true(),x) -> #f(gt(x,0()),double(x)) #4: #f(true(),x) -> #gt(x,0()) #5: #f(true(),x) -> #double(x) #6: #gt(s(x),s(y)) -> #gt(x,y) Number of SCCs: 3, DPs: 3, edges: 3 SCC { #6 } Removing DPs: Order(PosReal,>,Sum)... succeeded. s(x1) weight: (/ 1 2) + x1 gt(x1,x2) weight: 0 false() weight: 0 true() weight: 0 f(x1,x2) weight: 0 #doubleAkk(x1,x2) weight: 0 0() weight: 0 #double(x1) weight: 0 double(x1) weight: 0 doubleAkk(x1,x2) weight: 0 #gt(x1,x2) weight: x2 #f(x1,x2) weight: 0 Usable rules: { } Removed DPs: #6 Number of SCCs: 2, DPs: 2, edges: 2 SCC { #1 } Removing DPs: Order(PosReal,>,Sum)... succeeded. s(x1) weight: (/ 1 4) + x1 gt(x1,x2) weight: 0 false() weight: 0 true() weight: 0 f(x1,x2) weight: 0 #doubleAkk(x1,x2) weight: x1 0() weight: 0 #double(x1) weight: 0 double(x1) weight: 0 doubleAkk(x1,x2) weight: 0 #gt(x1,x2) weight: 0 #f(x1,x2) weight: 0 Usable rules: { } Removed DPs: #1 Number of SCCs: 1, DPs: 1, edges: 1 SCC { #3 } 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