176.63/45.31 YES 176.63/45.32 176.63/45.32 Problem: 176.63/45.32 a(x1) -> x1 176.63/45.32 a(b(x1)) -> b(c(a(x1))) 176.63/45.32 c(c(x1)) -> b(a(c(a(x1)))) 176.63/45.32 176.63/45.32 Proof: 176.63/45.32 String Reversal Processor: 176.63/45.32 a(x1) -> x1 176.63/45.32 b(a(x1)) -> a(c(b(x1))) 176.63/45.32 c(c(x1)) -> a(c(a(b(x1)))) 176.63/45.32 DP Processor: 176.63/45.32 DPs: 176.63/45.32 b#(a(x1)) -> b#(x1) 176.63/45.32 b#(a(x1)) -> c#(b(x1)) 176.63/45.32 b#(a(x1)) -> a#(c(b(x1))) 176.63/45.32 c#(c(x1)) -> b#(x1) 176.63/45.32 c#(c(x1)) -> a#(b(x1)) 176.63/45.32 c#(c(x1)) -> c#(a(b(x1))) 176.63/45.32 c#(c(x1)) -> a#(c(a(b(x1)))) 176.63/45.32 TRS: 176.63/45.32 a(x1) -> x1 176.63/45.32 b(a(x1)) -> a(c(b(x1))) 176.63/45.32 c(c(x1)) -> a(c(a(b(x1)))) 176.63/45.32 TDG Processor: 176.63/45.32 DPs: 176.63/45.32 b#(a(x1)) -> b#(x1) 176.63/45.32 b#(a(x1)) -> c#(b(x1)) 176.63/45.32 b#(a(x1)) -> a#(c(b(x1))) 176.63/45.32 c#(c(x1)) -> b#(x1) 176.63/45.32 c#(c(x1)) -> a#(b(x1)) 176.63/45.32 c#(c(x1)) -> c#(a(b(x1))) 176.63/45.32 c#(c(x1)) -> a#(c(a(b(x1)))) 176.63/45.32 TRS: 176.63/45.32 a(x1) -> x1 176.63/45.32 b(a(x1)) -> a(c(b(x1))) 176.63/45.32 c(c(x1)) -> a(c(a(b(x1)))) 176.63/45.32 graph: 176.63/45.32 c#(c(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> a#(c(a(b(x1)))) 176.63/45.32 c#(c(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) 176.63/45.32 c#(c(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> a#(b(x1)) 176.63/45.32 c#(c(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> b#(x1) 176.63/45.32 c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1))) 176.63/45.32 c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> c#(b(x1)) 176.63/45.32 c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 176.63/45.32 b#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(c(a(b(x1)))) 176.63/45.32 b#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> c#(a(b(x1))) 176.63/45.32 b#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(b(x1)) 176.63/45.32 b#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(x1) 176.63/45.32 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1))) 176.63/45.32 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(b(x1)) 176.63/45.32 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 176.63/45.32 SCC Processor: 176.63/45.32 #sccs: 1 176.63/45.32 #rules: 4 176.63/45.32 #arcs: 14/49 176.63/45.32 DPs: 176.63/45.32 c#(c(x1)) -> c#(a(b(x1))) 176.63/45.32 c#(c(x1)) -> b#(x1) 176.63/45.32 b#(a(x1)) -> b#(x1) 176.63/45.32 b#(a(x1)) -> c#(b(x1)) 176.63/45.32 TRS: 176.63/45.32 a(x1) -> x1 176.63/45.32 b(a(x1)) -> a(c(b(x1))) 176.63/45.32 c(c(x1)) -> a(c(a(b(x1)))) 176.63/45.32 Arctic Interpretation Processor: 176.63/45.32 dimension: 2 176.63/45.32 usable rules: 176.63/45.32 a(x1) -> x1 176.63/45.32 b(a(x1)) -> a(c(b(x1))) 176.63/45.32 c(c(x1)) -> a(c(a(b(x1)))) 176.63/45.32 interpretation: 176.63/45.32 [c#](x0) = [-& 1 ]x0 + [0], 176.63/45.32 176.63/45.32 [b#](x0) = [0 0]x0 + [0], 176.63/45.32 176.63/45.32 [-& 0 ] [0] 176.63/45.32 [c](x0) = [1 1 ]x0 + [3], 176.63/45.32 176.63/45.32 [0 -&] 176.63/45.32 [b](x0) = [0 -&]x0, 176.63/45.32 176.63/45.32 [1 -&] [3] 176.63/45.32 [a](x0) = [0 0 ]x0 + [0] 176.63/45.32 orientation: 176.63/45.32 c#(c(x1)) = [2 2]x1 + [4] >= [1 -&]x1 + [1] = c#(a(b(x1))) 176.63/45.32 176.63/45.32 c#(c(x1)) = [2 2]x1 + [4] >= [0 0]x1 + [0] = b#(x1) 176.63/45.32 176.63/45.32 b#(a(x1)) = [1 0]x1 + [3] >= [0 0]x1 + [0] = b#(x1) 176.63/45.32 176.63/45.32 b#(a(x1)) = [1 0]x1 + [3] >= [1 -&]x1 + [0] = c#(b(x1)) 176.63/45.32 176.63/45.32 [1 -&] [3] 176.63/45.32 a(x1) = [0 0 ]x1 + [0] >= x1 = x1 176.63/45.32 176.63/45.32 [1 -&] [3] [1 -&] [3] 176.63/45.32 b(a(x1)) = [1 -&]x1 + [3] >= [1 -&]x1 + [3] = a(c(b(x1))) 176.63/45.32 176.63/45.32 [1 1] [3] [1 -&] [3] 176.63/45.32 c(c(x1)) = [2 2]x1 + [4] >= [2 -&]x1 + [4] = a(c(a(b(x1)))) 176.63/45.32 problem: 176.63/45.32 DPs: 176.63/45.32 b#(a(x1)) -> b#(x1) 176.63/45.32 b#(a(x1)) -> c#(b(x1)) 176.63/45.32 TRS: 176.63/45.32 a(x1) -> x1 176.63/45.32 b(a(x1)) -> a(c(b(x1))) 176.63/45.32 c(c(x1)) -> a(c(a(b(x1)))) 176.63/45.32 Restore Modifier: 176.63/45.32 DPs: 176.63/45.32 b#(a(x1)) -> b#(x1) 176.63/45.32 b#(a(x1)) -> c#(b(x1)) 176.63/45.32 TRS: 176.63/45.32 a(x1) -> x1 176.63/45.32 b(a(x1)) -> a(c(b(x1))) 176.63/45.32 c(c(x1)) -> a(c(a(b(x1)))) 176.63/45.32 EDG Processor: 176.63/45.32 DPs: 176.63/45.32 b#(a(x1)) -> b#(x1) 176.63/45.32 b#(a(x1)) -> c#(b(x1)) 176.63/45.32 TRS: 176.63/45.32 a(x1) -> x1 176.63/45.32 b(a(x1)) -> a(c(b(x1))) 176.63/45.32 c(c(x1)) -> a(c(a(b(x1)))) 176.63/45.32 graph: 176.63/45.32 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 176.63/45.32 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(b(x1)) 176.63/45.32 SCC Processor: 176.63/45.32 #sccs: 1 176.63/45.32 #rules: 1 176.63/45.32 #arcs: 2/4 176.63/45.32 DPs: 176.63/45.32 b#(a(x1)) -> b#(x1) 176.63/45.32 TRS: 176.63/45.32 a(x1) -> x1 176.63/45.32 b(a(x1)) -> a(c(b(x1))) 176.63/45.32 c(c(x1)) -> a(c(a(b(x1)))) 176.63/45.32 Usable Rule Processor: 176.63/45.32 DPs: 176.63/45.32 b#(a(x1)) -> b#(x1) 176.63/45.32 TRS: 176.63/45.32 176.63/45.32 Arctic Interpretation Processor: 176.63/45.32 dimension: 3 176.63/45.32 usable rules: 176.63/45.32 176.63/45.32 interpretation: 176.63/45.32 [b#](x0) = [1 -& -&]x0, 176.63/45.32 176.63/45.32 [1 1 0] [0] 176.63/45.32 [a](x0) = [1 1 1]x0 + [1] 176.63/45.32 [0 1 1] [1] 176.63/45.32 orientation: 176.63/45.32 b#(a(x1)) = [2 2 1]x1 + [1] >= [1 -& -&]x1 = b#(x1) 176.63/45.32 problem: 176.63/45.32 DPs: 176.63/45.32 176.63/45.32 TRS: 176.63/45.32 176.63/45.32 Qed 178.05/45.32 EOF