192.29/49.16 YES 192.29/49.17 192.29/49.17 Problem: 192.29/49.17 a(x1) -> x1 192.29/49.17 a(b(c(x1))) -> b(c(c(a(x1)))) 192.29/49.17 c(x1) -> b(a(x1)) 192.29/49.17 192.29/49.17 Proof: 192.29/49.17 String Reversal Processor: 192.29/49.17 a(x1) -> x1 192.29/49.17 c(b(a(x1))) -> a(c(c(b(x1)))) 192.29/49.17 c(x1) -> a(b(x1)) 192.29/49.17 DP Processor: 192.29/49.17 DPs: 192.29/49.17 c#(b(a(x1))) -> c#(b(x1)) 192.29/49.17 c#(b(a(x1))) -> c#(c(b(x1))) 192.29/49.17 c#(b(a(x1))) -> a#(c(c(b(x1)))) 192.29/49.17 c#(x1) -> a#(b(x1)) 192.29/49.17 TRS: 192.29/49.17 a(x1) -> x1 192.29/49.17 c(b(a(x1))) -> a(c(c(b(x1)))) 192.29/49.17 c(x1) -> a(b(x1)) 192.29/49.17 TDG Processor: 192.29/49.17 DPs: 192.29/49.17 c#(b(a(x1))) -> c#(b(x1)) 192.29/49.17 c#(b(a(x1))) -> c#(c(b(x1))) 192.29/49.17 c#(b(a(x1))) -> a#(c(c(b(x1)))) 192.29/49.17 c#(x1) -> a#(b(x1)) 192.29/49.17 TRS: 192.29/49.17 a(x1) -> x1 192.29/49.17 c(b(a(x1))) -> a(c(c(b(x1)))) 192.29/49.17 c(x1) -> a(b(x1)) 192.29/49.17 graph: 192.29/49.17 c#(b(a(x1))) -> c#(b(x1)) -> c#(x1) -> a#(b(x1)) 192.29/49.17 c#(b(a(x1))) -> c#(b(x1)) -> c#(b(a(x1))) -> a#(c(c(b(x1)))) 192.29/49.17 c#(b(a(x1))) -> c#(b(x1)) -> c#(b(a(x1))) -> c#(c(b(x1))) 192.29/49.17 c#(b(a(x1))) -> c#(b(x1)) -> c#(b(a(x1))) -> c#(b(x1)) 192.29/49.17 c#(b(a(x1))) -> c#(c(b(x1))) -> c#(x1) -> a#(b(x1)) 192.29/49.17 c#(b(a(x1))) -> c#(c(b(x1))) -> c#(b(a(x1))) -> a#(c(c(b(x1)))) 192.29/49.17 c#(b(a(x1))) -> c#(c(b(x1))) -> c#(b(a(x1))) -> c#(c(b(x1))) 192.29/49.17 c#(b(a(x1))) -> c#(c(b(x1))) -> c#(b(a(x1))) -> c#(b(x1)) 192.29/49.17 SCC Processor: 192.29/49.17 #sccs: 1 192.29/49.17 #rules: 2 192.29/49.17 #arcs: 8/16 192.29/49.17 DPs: 192.29/49.17 c#(b(a(x1))) -> c#(b(x1)) 192.29/49.17 c#(b(a(x1))) -> c#(c(b(x1))) 192.29/49.17 TRS: 192.29/49.17 a(x1) -> x1 192.29/49.17 c(b(a(x1))) -> a(c(c(b(x1)))) 192.29/49.17 c(x1) -> a(b(x1)) 192.29/49.17 Arctic Interpretation Processor: 192.29/49.17 dimension: 3 192.29/49.17 usable rules: 192.29/49.17 a(x1) -> x1 192.29/49.17 c(b(a(x1))) -> a(c(c(b(x1)))) 192.29/49.17 c(x1) -> a(b(x1)) 192.29/49.17 interpretation: 192.29/49.17 [c#](x0) = [0 0 0]x0 + [0], 192.29/49.17 192.29/49.17 [-& 0 0 ] [0] 192.29/49.17 [b](x0) = [-& -& 0 ]x0 + [0] 192.29/49.17 [-& -& 0 ] [0], 192.29/49.17 192.29/49.17 [0 0 0] [0] 192.29/49.17 [c](x0) = [1 0 1]x0 + [1] 192.29/49.17 [0 0 0] [0], 192.29/49.17 192.29/49.17 [0 0 0] [0] 192.29/49.17 [a](x0) = [0 1 1]x0 + [1] 192.29/49.17 [0 0 0] [0] 192.29/49.17 orientation: 192.29/49.17 c#(b(a(x1))) = [0 1 1]x1 + [1] >= [-& 0 0 ]x1 + [0] = c#(b(x1)) 192.29/49.17 192.29/49.17 c#(b(a(x1))) = [0 1 1]x1 + [1] >= [-& 1 1 ]x1 + [1] = c#(c(b(x1))) 192.29/49.17 192.29/49.17 [0 0 0] [0] 192.29/49.17 a(x1) = [0 1 1]x1 + [1] >= x1 = x1 192.29/49.17 [0 0 0] [0] 192.29/49.17 192.29/49.17 [0 1 1] [1] [-& 1 1 ] [1] 192.29/49.17 c(b(a(x1))) = [1 2 2]x1 + [2] >= [-& 2 2 ]x1 + [2] = a(c(c(b(x1)))) 192.29/49.17 [0 1 1] [1] [-& 1 1 ] [1] 192.29/49.17 192.29/49.17 [0 0 0] [0] [-& 0 0 ] [0] 192.29/49.17 c(x1) = [1 0 1]x1 + [1] >= [-& 0 1 ]x1 + [1] = a(b(x1)) 192.29/49.17 [0 0 0] [0] [-& 0 0 ] [0] 192.29/49.17 problem: 192.29/49.17 DPs: 192.29/49.17 c#(b(a(x1))) -> c#(c(b(x1))) 192.29/49.17 TRS: 192.29/49.17 a(x1) -> x1 192.29/49.17 c(b(a(x1))) -> a(c(c(b(x1)))) 192.29/49.17 c(x1) -> a(b(x1)) 192.29/49.17 Restore Modifier: 192.29/49.17 DPs: 192.29/49.17 c#(b(a(x1))) -> c#(c(b(x1))) 192.29/49.17 TRS: 192.29/49.17 a(x1) -> x1 192.29/49.17 c(b(a(x1))) -> a(c(c(b(x1)))) 192.29/49.17 c(x1) -> a(b(x1)) 192.29/49.17 EDG Processor: 192.29/49.17 DPs: 192.29/49.17 c#(b(a(x1))) -> c#(c(b(x1))) 192.29/49.17 TRS: 192.29/49.17 a(x1) -> x1 192.29/49.17 c(b(a(x1))) -> a(c(c(b(x1)))) 192.29/49.17 c(x1) -> a(b(x1)) 192.29/49.17 graph: 192.29/49.17 c#(b(a(x1))) -> c#(c(b(x1))) -> c#(b(a(x1))) -> c#(c(b(x1))) 192.29/49.17 Arctic Interpretation Processor: 192.29/49.17 dimension: 2 192.29/49.17 usable rules: 192.29/49.17 a(x1) -> x1 192.29/49.17 c(b(a(x1))) -> a(c(c(b(x1)))) 192.29/49.17 c(x1) -> a(b(x1)) 192.29/49.17 interpretation: 192.29/49.17 [c#](x0) = [-& 0 ]x0 + [0], 192.29/49.17 192.29/49.17 [-& -&] [0] 192.29/49.17 [b](x0) = [0 -&]x0 + [0], 192.29/49.17 192.29/49.17 [0 1] [1] 192.29/49.17 [c](x0) = [0 0]x0 + [0], 192.29/49.17 192.29/49.17 [1 0] [1] 192.29/49.17 [a](x0) = [0 0]x0 + [0] 192.29/49.17 orientation: 192.29/49.17 c#(b(a(x1))) = [1 0]x1 + [1] >= [0 -&]x1 + [0] = c#(c(b(x1))) 192.29/49.17 192.29/49.17 [1 0] [1] 192.29/49.17 a(x1) = [0 0]x1 + [0] >= x1 = x1 192.29/49.17 192.29/49.17 [2 1] [2] [2 -&] [2] 192.29/49.17 c(b(a(x1))) = [1 0]x1 + [1] >= [1 -&]x1 + [1] = a(c(c(b(x1)))) 192.29/49.17 192.29/49.17 [0 1] [1] [0 -&] [1] 192.29/49.17 c(x1) = [0 0]x1 + [0] >= [0 -&]x1 + [0] = a(b(x1)) 192.29/49.17 problem: 192.29/49.17 DPs: 192.29/49.17 192.29/49.17 TRS: 192.29/49.17 a(x1) -> x1 192.29/49.17 c(b(a(x1))) -> a(c(c(b(x1)))) 192.29/49.17 c(x1) -> a(b(x1)) 192.29/49.17 Qed 192.29/49.17 EOF