177.96/45.68 YES 177.96/45.69 177.96/45.69 Problem: 177.96/45.69 p(0(x1)) -> 0(s(s(p(x1)))) 177.96/45.69 p(s(x1)) -> x1 177.96/45.69 p(p(s(x1))) -> p(x1) 177.96/45.69 f(s(x1)) -> g(s(x1)) 177.96/45.69 g(x1) -> i(s(half(x1))) 177.96/45.69 i(x1) -> f(p(x1)) 177.96/45.69 half(0(x1)) -> 0(s(s(half(x1)))) 177.96/45.69 half(s(s(x1))) -> s(half(p(p(s(s(x1)))))) 177.96/45.69 0(x1) -> x1 177.96/45.69 rd(0(x1)) -> 0(0(0(0(0(0(rd(x1))))))) 177.96/45.69 177.96/45.69 Proof: 177.96/45.69 Matrix Interpretation Processor: dim=1 177.96/45.69 177.96/45.69 interpretation: 177.96/45.69 [rd](x0) = 8x0 + 8, 177.96/45.69 177.96/45.69 [i](x0) = x0 + 1, 177.96/45.69 177.96/45.69 [half](x0) = x0, 177.96/45.69 177.96/45.69 [g](x0) = x0 + 1, 177.96/45.69 177.96/45.69 [f](x0) = x0 + 1, 177.96/45.69 177.96/45.69 [s](x0) = x0, 177.96/45.69 177.96/45.69 [p](x0) = x0, 177.96/45.69 177.96/45.69 [0](x0) = x0 + 1 177.96/45.69 orientation: 177.96/45.69 p(0(x1)) = x1 + 1 >= x1 + 1 = 0(s(s(p(x1)))) 177.96/45.69 177.96/45.69 p(s(x1)) = x1 >= x1 = x1 177.96/45.69 177.96/45.69 p(p(s(x1))) = x1 >= x1 = p(x1) 177.96/45.69 177.96/45.69 f(s(x1)) = x1 + 1 >= x1 + 1 = g(s(x1)) 177.96/45.69 177.96/45.69 g(x1) = x1 + 1 >= x1 + 1 = i(s(half(x1))) 177.96/45.69 177.96/45.69 i(x1) = x1 + 1 >= x1 + 1 = f(p(x1)) 177.96/45.69 177.96/45.69 half(0(x1)) = x1 + 1 >= x1 + 1 = 0(s(s(half(x1)))) 177.96/45.69 177.96/45.69 half(s(s(x1))) = x1 >= x1 = s(half(p(p(s(s(x1)))))) 177.96/45.69 177.96/45.69 0(x1) = x1 + 1 >= x1 = x1 177.96/45.69 177.96/45.69 rd(0(x1)) = 8x1 + 16 >= 8x1 + 14 = 0(0(0(0(0(0(rd(x1))))))) 177.96/45.69 problem: 177.96/45.69 p(0(x1)) -> 0(s(s(p(x1)))) 177.96/45.69 p(s(x1)) -> x1 177.96/45.69 p(p(s(x1))) -> p(x1) 177.96/45.69 f(s(x1)) -> g(s(x1)) 177.96/45.69 g(x1) -> i(s(half(x1))) 177.96/45.69 i(x1) -> f(p(x1)) 177.96/45.69 half(0(x1)) -> 0(s(s(half(x1)))) 177.96/45.69 half(s(s(x1))) -> s(half(p(p(s(s(x1)))))) 177.96/45.69 String Reversal Processor: 177.96/45.69 0(p(x1)) -> p(s(s(0(x1)))) 177.96/45.69 s(p(x1)) -> x1 177.96/45.69 s(p(p(x1))) -> p(x1) 177.96/45.69 s(f(x1)) -> s(g(x1)) 177.96/45.69 g(x1) -> half(s(i(x1))) 177.96/45.69 i(x1) -> p(f(x1)) 177.96/45.69 0(half(x1)) -> half(s(s(0(x1)))) 177.96/45.69 s(s(half(x1))) -> s(s(p(p(half(s(x1)))))) 177.96/45.69 DP Processor: 177.96/45.69 DPs: 177.96/45.69 0#(p(x1)) -> 0#(x1) 177.96/45.69 0#(p(x1)) -> s#(0(x1)) 177.96/45.69 0#(p(x1)) -> s#(s(0(x1))) 177.96/45.69 s#(f(x1)) -> g#(x1) 177.96/45.69 s#(f(x1)) -> s#(g(x1)) 177.96/45.69 g#(x1) -> i#(x1) 177.96/45.69 g#(x1) -> s#(i(x1)) 177.96/45.69 0#(half(x1)) -> 0#(x1) 177.96/45.69 0#(half(x1)) -> s#(0(x1)) 177.96/45.69 0#(half(x1)) -> s#(s(0(x1))) 177.96/45.69 s#(s(half(x1))) -> s#(x1) 177.96/45.69 s#(s(half(x1))) -> s#(p(p(half(s(x1))))) 177.96/45.69 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) 177.96/45.69 TRS: 177.96/45.69 0(p(x1)) -> p(s(s(0(x1)))) 177.96/45.69 s(p(x1)) -> x1 177.96/45.69 s(p(p(x1))) -> p(x1) 177.96/45.69 s(f(x1)) -> s(g(x1)) 177.96/45.69 g(x1) -> half(s(i(x1))) 177.96/45.69 i(x1) -> p(f(x1)) 177.96/45.69 0(half(x1)) -> half(s(s(0(x1)))) 177.96/45.69 s(s(half(x1))) -> s(s(p(p(half(s(x1)))))) 177.96/45.69 TDG Processor: 177.96/45.69 DPs: 177.96/45.69 0#(p(x1)) -> 0#(x1) 177.96/45.69 0#(p(x1)) -> s#(0(x1)) 177.96/45.69 0#(p(x1)) -> s#(s(0(x1))) 177.96/45.69 s#(f(x1)) -> g#(x1) 177.96/45.69 s#(f(x1)) -> s#(g(x1)) 177.96/45.69 g#(x1) -> i#(x1) 177.96/45.69 g#(x1) -> s#(i(x1)) 177.96/45.69 0#(half(x1)) -> 0#(x1) 177.96/45.69 0#(half(x1)) -> s#(0(x1)) 177.96/45.69 0#(half(x1)) -> s#(s(0(x1))) 177.96/45.69 s#(s(half(x1))) -> s#(x1) 177.96/45.69 s#(s(half(x1))) -> s#(p(p(half(s(x1))))) 177.96/45.69 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) 177.96/45.69 TRS: 177.96/45.69 0(p(x1)) -> p(s(s(0(x1)))) 177.96/45.69 s(p(x1)) -> x1 177.96/45.69 s(p(p(x1))) -> p(x1) 177.96/45.69 s(f(x1)) -> s(g(x1)) 177.96/45.69 g(x1) -> half(s(i(x1))) 177.96/45.69 i(x1) -> p(f(x1)) 177.96/45.69 0(half(x1)) -> half(s(s(0(x1)))) 177.96/45.69 s(s(half(x1))) -> s(s(p(p(half(s(x1)))))) 177.96/45.69 graph: 177.96/45.69 g#(x1) -> s#(i(x1)) -> s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) 177.96/45.69 g#(x1) -> s#(i(x1)) -> s#(s(half(x1))) -> s#(p(p(half(s(x1))))) 177.96/45.69 g#(x1) -> s#(i(x1)) -> s#(s(half(x1))) -> s#(x1) 177.96/45.69 g#(x1) -> s#(i(x1)) -> s#(f(x1)) -> s#(g(x1)) 177.96/45.69 g#(x1) -> s#(i(x1)) -> s#(f(x1)) -> g#(x1) 177.96/45.69 s#(f(x1)) -> g#(x1) -> g#(x1) -> s#(i(x1)) 177.96/45.69 s#(f(x1)) -> g#(x1) -> g#(x1) -> i#(x1) 177.96/45.69 s#(f(x1)) -> s#(g(x1)) -> s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) 177.96/45.69 s#(f(x1)) -> s#(g(x1)) -> s#(s(half(x1))) -> s#(p(p(half(s(x1))))) 177.96/45.69 s#(f(x1)) -> s#(g(x1)) -> s#(s(half(x1))) -> s#(x1) 177.96/45.69 s#(f(x1)) -> s#(g(x1)) -> s#(f(x1)) -> s#(g(x1)) 177.96/45.69 s#(f(x1)) -> s#(g(x1)) -> s#(f(x1)) -> g#(x1) 177.96/45.69 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) -> 177.96/45.69 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) 177.96/45.69 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) -> 177.96/45.69 s#(s(half(x1))) -> s#(p(p(half(s(x1))))) 177.96/45.69 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) -> 177.96/45.69 s#(s(half(x1))) -> s#(x1) 177.96/45.69 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) -> 177.96/45.69 s#(f(x1)) -> s#(g(x1)) 177.96/45.69 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) -> 177.96/45.69 s#(f(x1)) -> g#(x1) 177.96/45.69 s#(s(half(x1))) -> s#(p(p(half(s(x1))))) -> 178.81/45.70 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) 178.81/45.70 s#(s(half(x1))) -> s#(p(p(half(s(x1))))) -> 178.81/45.70 s#(s(half(x1))) -> s#(p(p(half(s(x1))))) 178.81/45.70 s#(s(half(x1))) -> s#(p(p(half(s(x1))))) -> 178.81/45.70 s#(s(half(x1))) -> s#(x1) 178.81/45.70 s#(s(half(x1))) -> s#(p(p(half(s(x1))))) -> 178.81/45.70 s#(f(x1)) -> s#(g(x1)) 178.81/45.70 s#(s(half(x1))) -> s#(p(p(half(s(x1))))) -> s#(f(x1)) -> g#(x1) 178.81/45.70 s#(s(half(x1))) -> s#(x1) -> 178.81/45.70 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) 178.81/45.70 s#(s(half(x1))) -> s#(x1) -> 178.81/45.70 s#(s(half(x1))) -> s#(p(p(half(s(x1))))) 178.81/45.70 s#(s(half(x1))) -> s#(x1) -> s#(s(half(x1))) -> s#(x1) 178.81/45.70 s#(s(half(x1))) -> s#(x1) -> s#(f(x1)) -> s#(g(x1)) 178.81/45.70 s#(s(half(x1))) -> s#(x1) -> s#(f(x1)) -> g#(x1) 178.81/45.70 0#(half(x1)) -> s#(s(0(x1))) -> 178.81/45.70 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) 178.81/45.70 0#(half(x1)) -> s#(s(0(x1))) -> 178.81/45.70 s#(s(half(x1))) -> s#(p(p(half(s(x1))))) 178.81/45.70 0#(half(x1)) -> s#(s(0(x1))) -> s#(s(half(x1))) -> s#(x1) 178.81/45.70 0#(half(x1)) -> s#(s(0(x1))) -> s#(f(x1)) -> s#(g(x1)) 178.81/45.70 0#(half(x1)) -> s#(s(0(x1))) -> s#(f(x1)) -> g#(x1) 178.81/45.70 0#(half(x1)) -> s#(0(x1)) -> 178.81/45.70 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) 178.81/45.70 0#(half(x1)) -> s#(0(x1)) -> 178.81/45.70 s#(s(half(x1))) -> s#(p(p(half(s(x1))))) 178.81/45.70 0#(half(x1)) -> s#(0(x1)) -> s#(s(half(x1))) -> s#(x1) 178.81/45.70 0#(half(x1)) -> s#(0(x1)) -> s#(f(x1)) -> s#(g(x1)) 178.81/45.70 0#(half(x1)) -> s#(0(x1)) -> s#(f(x1)) -> g#(x1) 178.81/45.70 0#(half(x1)) -> 0#(x1) -> 0#(half(x1)) -> s#(s(0(x1))) 178.81/45.70 0#(half(x1)) -> 0#(x1) -> 0#(half(x1)) -> s#(0(x1)) 178.81/45.70 0#(half(x1)) -> 0#(x1) -> 0#(half(x1)) -> 0#(x1) 178.81/45.70 0#(half(x1)) -> 0#(x1) -> 0#(p(x1)) -> s#(s(0(x1))) 178.81/45.70 0#(half(x1)) -> 0#(x1) -> 0#(p(x1)) -> s#(0(x1)) 178.81/45.70 0#(half(x1)) -> 0#(x1) -> 0#(p(x1)) -> 0#(x1) 178.81/45.70 0#(p(x1)) -> s#(s(0(x1))) -> 178.81/45.70 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) 178.81/45.70 0#(p(x1)) -> s#(s(0(x1))) -> 178.81/45.70 s#(s(half(x1))) -> s#(p(p(half(s(x1))))) 178.81/45.70 0#(p(x1)) -> s#(s(0(x1))) -> s#(s(half(x1))) -> s#(x1) 178.81/45.70 0#(p(x1)) -> s#(s(0(x1))) -> s#(f(x1)) -> s#(g(x1)) 178.81/45.70 0#(p(x1)) -> s#(s(0(x1))) -> s#(f(x1)) -> g#(x1) 178.81/45.70 0#(p(x1)) -> s#(0(x1)) -> s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) 178.81/45.70 0#(p(x1)) -> s#(0(x1)) -> s#(s(half(x1))) -> s#(p(p(half(s(x1))))) 178.81/45.70 0#(p(x1)) -> s#(0(x1)) -> s#(s(half(x1))) -> s#(x1) 178.81/45.70 0#(p(x1)) -> s#(0(x1)) -> s#(f(x1)) -> s#(g(x1)) 178.81/45.70 0#(p(x1)) -> s#(0(x1)) -> s#(f(x1)) -> g#(x1) 178.81/45.70 0#(p(x1)) -> 0#(x1) -> 0#(half(x1)) -> s#(s(0(x1))) 178.81/45.70 0#(p(x1)) -> 0#(x1) -> 0#(half(x1)) -> s#(0(x1)) 178.81/45.70 0#(p(x1)) -> 0#(x1) -> 0#(half(x1)) -> 0#(x1) 178.81/45.70 0#(p(x1)) -> 0#(x1) -> 0#(p(x1)) -> s#(s(0(x1))) 178.81/45.70 0#(p(x1)) -> 0#(x1) -> 0#(p(x1)) -> s#(0(x1)) 178.81/45.70 0#(p(x1)) -> 0#(x1) -> 0#(p(x1)) -> 0#(x1) 178.81/45.70 EDG Processor: 178.81/45.70 DPs: 178.81/45.70 0#(p(x1)) -> 0#(x1) 178.81/45.70 0#(p(x1)) -> s#(0(x1)) 178.81/45.70 0#(p(x1)) -> s#(s(0(x1))) 178.81/45.70 s#(f(x1)) -> g#(x1) 178.81/45.70 s#(f(x1)) -> s#(g(x1)) 178.81/45.70 g#(x1) -> i#(x1) 178.81/45.70 g#(x1) -> s#(i(x1)) 178.81/45.70 0#(half(x1)) -> 0#(x1) 178.81/45.70 0#(half(x1)) -> s#(0(x1)) 178.81/45.70 0#(half(x1)) -> s#(s(0(x1))) 178.81/45.70 s#(s(half(x1))) -> s#(x1) 178.81/45.70 s#(s(half(x1))) -> s#(p(p(half(s(x1))))) 178.81/45.70 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) 178.81/45.70 TRS: 178.81/45.70 0(p(x1)) -> p(s(s(0(x1)))) 178.81/45.70 s(p(x1)) -> x1 178.81/45.70 s(p(p(x1))) -> p(x1) 178.81/45.70 s(f(x1)) -> s(g(x1)) 178.81/45.70 g(x1) -> half(s(i(x1))) 178.81/45.70 i(x1) -> p(f(x1)) 178.81/45.70 0(half(x1)) -> half(s(s(0(x1)))) 178.81/45.70 s(s(half(x1))) -> s(s(p(p(half(s(x1)))))) 178.81/45.70 graph: 178.81/45.70 s#(f(x1)) -> g#(x1) -> g#(x1) -> i#(x1) 178.81/45.70 s#(f(x1)) -> g#(x1) -> g#(x1) -> s#(i(x1)) 178.81/45.70 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) -> 178.81/45.70 s#(f(x1)) -> g#(x1) 178.81/45.70 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) -> 178.81/45.70 s#(f(x1)) -> s#(g(x1)) 178.81/45.70 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) -> 178.81/45.70 s#(s(half(x1))) -> s#(x1) 178.81/45.70 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) -> 178.81/45.70 s#(s(half(x1))) -> s#(p(p(half(s(x1))))) 178.81/45.70 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) -> 178.81/45.70 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) 178.81/45.70 s#(s(half(x1))) -> s#(x1) -> s#(f(x1)) -> g#(x1) 178.81/45.71 s#(s(half(x1))) -> s#(x1) -> s#(f(x1)) -> s#(g(x1)) 178.81/45.71 s#(s(half(x1))) -> s#(x1) -> s#(s(half(x1))) -> s#(x1) 178.81/45.71 s#(s(half(x1))) -> s#(x1) -> 178.81/45.71 s#(s(half(x1))) -> s#(p(p(half(s(x1))))) 178.81/45.71 s#(s(half(x1))) -> s#(x1) -> 178.81/45.71 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) 178.81/45.71 0#(half(x1)) -> s#(s(0(x1))) -> s#(f(x1)) -> g#(x1) 178.81/45.71 0#(half(x1)) -> s#(s(0(x1))) -> s#(f(x1)) -> s#(g(x1)) 178.81/45.71 0#(half(x1)) -> s#(s(0(x1))) -> s#(s(half(x1))) -> s#(x1) 178.81/45.71 0#(half(x1)) -> s#(s(0(x1))) -> 178.81/45.71 s#(s(half(x1))) -> s#(p(p(half(s(x1))))) 178.81/45.71 0#(half(x1)) -> s#(s(0(x1))) -> 178.81/45.71 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) 178.81/45.71 0#(half(x1)) -> 0#(x1) -> 0#(p(x1)) -> 0#(x1) 178.81/45.71 0#(half(x1)) -> 0#(x1) -> 0#(p(x1)) -> s#(0(x1)) 178.81/45.71 0#(half(x1)) -> 0#(x1) -> 0#(p(x1)) -> s#(s(0(x1))) 178.81/45.71 0#(half(x1)) -> 0#(x1) -> 0#(half(x1)) -> 0#(x1) 178.81/45.71 0#(half(x1)) -> 0#(x1) -> 0#(half(x1)) -> s#(0(x1)) 178.81/45.71 0#(half(x1)) -> 0#(x1) -> 0#(half(x1)) -> s#(s(0(x1))) 178.81/45.71 0#(p(x1)) -> s#(s(0(x1))) -> s#(f(x1)) -> g#(x1) 178.81/45.71 0#(p(x1)) -> s#(s(0(x1))) -> s#(f(x1)) -> s#(g(x1)) 178.81/45.71 0#(p(x1)) -> s#(s(0(x1))) -> s#(s(half(x1))) -> s#(x1) 178.81/45.71 0#(p(x1)) -> s#(s(0(x1))) -> 178.81/45.71 s#(s(half(x1))) -> s#(p(p(half(s(x1))))) 178.81/45.71 0#(p(x1)) -> s#(s(0(x1))) -> s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) 178.81/45.71 0#(p(x1)) -> 0#(x1) -> 0#(p(x1)) -> 0#(x1) 178.81/45.71 0#(p(x1)) -> 0#(x1) -> 0#(p(x1)) -> s#(0(x1)) 178.81/45.71 0#(p(x1)) -> 0#(x1) -> 0#(p(x1)) -> s#(s(0(x1))) 178.81/45.71 0#(p(x1)) -> 0#(x1) -> 0#(half(x1)) -> 0#(x1) 178.81/45.71 0#(p(x1)) -> 0#(x1) -> 0#(half(x1)) -> s#(0(x1)) 178.81/45.71 0#(p(x1)) -> 0#(x1) -> 0#(half(x1)) -> s#(s(0(x1))) 178.81/45.71 SCC Processor: 178.81/45.71 #sccs: 2 178.81/45.71 #rules: 4 178.81/45.71 #arcs: 34/169 178.81/45.71 DPs: 178.81/45.71 0#(half(x1)) -> 0#(x1) 178.81/45.71 0#(p(x1)) -> 0#(x1) 178.81/45.71 TRS: 178.81/45.71 0(p(x1)) -> p(s(s(0(x1)))) 178.81/45.71 s(p(x1)) -> x1 178.81/45.71 s(p(p(x1))) -> p(x1) 178.81/45.71 s(f(x1)) -> s(g(x1)) 178.81/45.71 g(x1) -> half(s(i(x1))) 178.81/45.71 i(x1) -> p(f(x1)) 178.81/45.71 0(half(x1)) -> half(s(s(0(x1)))) 178.81/45.71 s(s(half(x1))) -> s(s(p(p(half(s(x1)))))) 178.81/45.71 Usable Rule Processor: 178.81/45.71 DPs: 178.81/45.71 0#(half(x1)) -> 0#(x1) 178.81/45.71 0#(p(x1)) -> 0#(x1) 178.81/45.71 TRS: 178.81/45.71 178.81/45.71 Arctic Interpretation Processor: 178.81/45.71 dimension: 1 178.81/45.71 usable rules: 178.81/45.71 178.81/45.71 interpretation: 178.81/45.71 [0#](x0) = x0, 178.81/45.71 178.81/45.71 [half](x0) = x0, 178.81/45.71 178.81/45.71 [p](x0) = 1x0 + 9 178.81/45.71 orientation: 178.81/45.71 0#(half(x1)) = x1 >= x1 = 0#(x1) 178.81/45.71 178.81/45.71 0#(p(x1)) = 1x1 + 9 >= x1 = 0#(x1) 178.81/45.71 problem: 178.81/45.71 DPs: 178.81/45.71 0#(half(x1)) -> 0#(x1) 178.81/45.71 TRS: 178.81/45.71 178.81/45.71 Restore Modifier: 178.81/45.71 DPs: 178.81/45.71 0#(half(x1)) -> 0#(x1) 178.81/45.71 TRS: 178.81/45.71 0(p(x1)) -> p(s(s(0(x1)))) 178.81/45.71 s(p(x1)) -> x1 178.81/45.71 s(p(p(x1))) -> p(x1) 178.81/45.71 s(f(x1)) -> s(g(x1)) 178.81/45.71 g(x1) -> half(s(i(x1))) 178.81/45.71 i(x1) -> p(f(x1)) 178.81/45.71 0(half(x1)) -> half(s(s(0(x1)))) 178.81/45.71 s(s(half(x1))) -> s(s(p(p(half(s(x1)))))) 178.81/45.71 EDG Processor: 178.81/45.71 DPs: 178.81/45.71 0#(half(x1)) -> 0#(x1) 178.81/45.71 TRS: 178.81/45.71 0(p(x1)) -> p(s(s(0(x1)))) 178.81/45.71 s(p(x1)) -> x1 178.81/45.71 s(p(p(x1))) -> p(x1) 178.81/45.71 s(f(x1)) -> s(g(x1)) 178.81/45.71 g(x1) -> half(s(i(x1))) 178.81/45.71 i(x1) -> p(f(x1)) 178.81/45.71 0(half(x1)) -> half(s(s(0(x1)))) 178.81/45.71 s(s(half(x1))) -> s(s(p(p(half(s(x1)))))) 178.81/45.71 graph: 178.81/45.71 0#(half(x1)) -> 0#(x1) -> 0#(half(x1)) -> 0#(x1) 178.81/45.71 Usable Rule Processor: 178.81/45.71 DPs: 178.81/45.71 0#(half(x1)) -> 0#(x1) 178.81/45.71 TRS: 178.81/45.71 178.81/45.71 Arctic Interpretation Processor: 178.81/45.71 dimension: 4 178.81/45.71 usable rules: 178.81/45.71 178.81/45.71 interpretation: 178.81/45.71 [0#](x0) = [0 -& -& -&]x0, 178.81/45.71 178.81/45.71 [1 0 0 0] [0] 178.81/45.71 [0 0 0 0] [0] 178.81/45.71 [half](x0) = [1 0 0 0]x0 + [0] 178.81/45.71 [0 0 0 0] [0] 178.81/45.71 orientation: 178.81/45.71 0#(half(x1)) = [1 0 0 0]x1 + [0] >= [0 -& -& -&]x1 = 0#(x1) 178.81/45.71 problem: 178.81/45.71 DPs: 178.81/45.71 178.81/45.71 TRS: 178.81/45.71 178.81/45.71 Qed 178.81/45.71 178.81/45.71 DPs: 178.81/45.71 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) 178.81/45.71 s#(s(half(x1))) -> s#(x1) 178.81/45.71 TRS: 178.81/45.71 0(p(x1)) -> p(s(s(0(x1)))) 178.81/45.71 s(p(x1)) -> x1 178.81/45.71 s(p(p(x1))) -> p(x1) 178.81/45.71 s(f(x1)) -> s(g(x1)) 178.81/45.71 g(x1) -> half(s(i(x1))) 178.81/45.71 i(x1) -> p(f(x1)) 178.81/45.71 0(half(x1)) -> half(s(s(0(x1)))) 178.81/45.71 s(s(half(x1))) -> s(s(p(p(half(s(x1)))))) 178.81/45.71 Usable Rule Processor: 178.81/45.71 DPs: 178.81/45.71 s#(s(half(x1))) -> s#(s(p(p(half(s(x1)))))) 178.81/45.71 s#(s(half(x1))) -> s#(x1) 178.81/45.71 TRS: 178.81/45.71 s(p(x1)) -> x1 178.81/45.71 s(p(p(x1))) -> p(x1) 178.81/45.71 s(f(x1)) -> s(g(x1)) 178.81/45.71 s(s(half(x1))) -> s(s(p(p(half(s(x1)))))) 178.81/45.71 g(x1) -> half(s(i(x1))) 178.81/45.71 i(x1) -> p(f(x1)) 178.81/45.71 Bounds Processor: 178.81/45.71 bound: 0 178.81/45.71 enrichment: match-dp 178.81/45.71 automaton: 178.81/45.71 final states: {1} 178.81/45.71 transitions: 178.81/45.71 f0(35) -> 36* 178.81/45.71 f120() -> 2* 178.81/45.71 s{#,0}(7) -> 1* 178.81/45.71 s0(25) -> 26* 178.81/45.71 s0(22) -> 23* 178.81/45.71 s0(2) -> 3* 178.81/45.71 s0(41) -> 42* 178.81/45.71 s0(6) -> 7* 178.81/45.71 p0(5) -> 6* 178.81/45.71 p0(17) -> 18* 178.81/45.71 p0(4) -> 5* 178.81/45.71 p0(36) -> 37* 178.81/45.71 half0(26) -> 27* 178.81/45.71 half0(3) -> 4* 178.81/45.71 g0(21) -> 22* 178.81/45.71 i0(24) -> 25* 178.81/45.71 2 -> 21,17,3 178.81/45.71 4 -> 42* 178.81/45.71 5 -> 7* 178.81/45.71 7 -> 41* 178.81/45.71 18 -> 3* 178.81/45.71 21 -> 24* 178.81/45.71 23 -> 3* 178.81/45.71 24 -> 35* 178.81/45.71 27 -> 22* 178.81/45.71 36 -> 26* 178.81/45.71 37 -> 25* 178.81/45.71 42 -> 3* 178.81/45.71 problem: 178.81/45.71 DPs: 178.81/45.71 s#(s(half(x1))) -> s#(x1) 178.81/45.71 TRS: 178.81/45.71 s(p(x1)) -> x1 178.81/45.71 s(p(p(x1))) -> p(x1) 178.81/45.71 s(f(x1)) -> s(g(x1)) 178.81/45.71 s(s(half(x1))) -> s(s(p(p(half(s(x1)))))) 178.81/45.71 g(x1) -> half(s(i(x1))) 178.81/45.71 i(x1) -> p(f(x1)) 178.81/45.71 Restore Modifier: 178.81/45.71 DPs: 178.81/45.71 s#(s(half(x1))) -> s#(x1) 178.81/45.71 TRS: 178.81/45.71 0(p(x1)) -> p(s(s(0(x1)))) 178.81/45.71 s(p(x1)) -> x1 178.81/45.71 s(p(p(x1))) -> p(x1) 178.81/45.71 s(f(x1)) -> s(g(x1)) 178.81/45.71 g(x1) -> half(s(i(x1))) 178.81/45.71 i(x1) -> p(f(x1)) 178.81/45.71 0(half(x1)) -> half(s(s(0(x1)))) 178.81/45.71 s(s(half(x1))) -> s(s(p(p(half(s(x1)))))) 178.81/45.71 EDG Processor: 178.81/45.71 DPs: 178.81/45.71 s#(s(half(x1))) -> s#(x1) 178.81/45.71 TRS: 178.81/45.71 0(p(x1)) -> p(s(s(0(x1)))) 178.81/45.71 s(p(x1)) -> x1 178.81/45.71 s(p(p(x1))) -> p(x1) 178.81/45.71 s(f(x1)) -> s(g(x1)) 178.81/45.71 g(x1) -> half(s(i(x1))) 178.81/45.71 i(x1) -> p(f(x1)) 178.81/45.71 0(half(x1)) -> half(s(s(0(x1)))) 178.81/45.71 s(s(half(x1))) -> s(s(p(p(half(s(x1)))))) 178.81/45.71 graph: 178.81/45.71 s#(s(half(x1))) -> s#(x1) -> s#(s(half(x1))) -> s#(x1) 178.81/45.71 Usable Rule Processor: 178.81/45.71 DPs: 178.81/45.71 s#(s(half(x1))) -> s#(x1) 178.81/45.71 TRS: 178.81/45.71 178.81/45.71 Bounds Processor: 178.81/45.71 bound: 0 178.81/45.71 enrichment: match-dp 178.81/45.71 automaton: 178.81/45.71 final states: {1} 178.81/45.71 transitions: 178.81/45.71 s{#,0}(2) -> 1* 178.81/45.71 f210() -> 2* 178.81/45.71 problem: 178.81/45.71 DPs: 178.81/45.71 178.81/45.71 TRS: 178.81/45.71 178.81/45.71 Qed 178.81/45.72 EOF