174.91/44.75 YES 174.91/44.76 174.91/44.76 Problem: 174.91/44.76 a(x1) -> x1 174.91/44.76 a(b(x1)) -> b(a(c(x1))) 174.91/44.76 b(b(x1)) -> x1 174.91/44.76 c(c(x1)) -> b(a(x1)) 174.91/44.76 174.91/44.76 Proof: 174.91/44.76 String Reversal Processor: 174.91/44.76 a(x1) -> x1 174.91/44.76 b(a(x1)) -> c(a(b(x1))) 174.91/44.76 b(b(x1)) -> x1 174.91/44.76 c(c(x1)) -> a(b(x1)) 174.91/44.76 DP Processor: 174.91/44.76 DPs: 174.91/44.76 b#(a(x1)) -> b#(x1) 174.91/44.76 b#(a(x1)) -> a#(b(x1)) 174.91/44.76 b#(a(x1)) -> c#(a(b(x1))) 174.91/44.76 c#(c(x1)) -> b#(x1) 174.91/44.76 c#(c(x1)) -> a#(b(x1)) 174.91/44.76 TRS: 174.91/44.76 a(x1) -> x1 174.91/44.76 b(a(x1)) -> c(a(b(x1))) 174.91/44.76 b(b(x1)) -> x1 174.91/44.76 c(c(x1)) -> a(b(x1)) 174.91/44.76 TDG Processor: 174.91/44.76 DPs: 174.91/44.76 b#(a(x1)) -> b#(x1) 174.91/44.76 b#(a(x1)) -> a#(b(x1)) 174.91/44.76 b#(a(x1)) -> c#(a(b(x1))) 174.91/44.76 c#(c(x1)) -> b#(x1) 174.91/44.76 c#(c(x1)) -> a#(b(x1)) 174.91/44.76 TRS: 174.91/44.76 a(x1) -> x1 174.91/44.76 b(a(x1)) -> c(a(b(x1))) 174.91/44.76 b(b(x1)) -> x1 174.91/44.76 c(c(x1)) -> a(b(x1)) 174.91/44.76 graph: 174.91/44.76 c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1))) 174.91/44.76 c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1)) 174.91/44.76 c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 174.91/44.76 b#(a(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> a#(b(x1)) 174.91/44.76 b#(a(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> b#(x1) 174.91/44.76 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1))) 174.91/44.76 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1)) 174.91/44.76 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 174.91/44.76 SCC Processor: 174.91/44.76 #sccs: 1 174.91/44.76 #rules: 3 174.91/44.76 #arcs: 8/25 174.91/44.76 DPs: 174.91/44.76 c#(c(x1)) -> b#(x1) 174.91/44.76 b#(a(x1)) -> b#(x1) 174.91/44.76 b#(a(x1)) -> c#(a(b(x1))) 174.91/44.76 TRS: 174.91/44.76 a(x1) -> x1 174.91/44.76 b(a(x1)) -> c(a(b(x1))) 174.91/44.76 b(b(x1)) -> x1 174.91/44.76 c(c(x1)) -> a(b(x1)) 174.91/44.76 Arctic Interpretation Processor: 174.91/44.76 dimension: 2 174.91/44.76 usable rules: 174.91/44.76 a(x1) -> x1 174.91/44.76 b(a(x1)) -> c(a(b(x1))) 174.91/44.76 b(b(x1)) -> x1 174.91/44.76 c(c(x1)) -> a(b(x1)) 174.91/44.76 interpretation: 174.91/44.76 [c#](x0) = [1 1]x0 + [0], 174.91/44.76 174.91/44.76 [b#](x0) = [0 1]x0, 174.91/44.76 174.91/44.76 [0 0 ] [0] 174.91/44.76 [c](x0) = [1 -&]x0 + [3], 174.91/44.76 174.91/44.76 [-& 0 ] [1] 174.91/44.76 [b](x0) = [0 0 ]x0 + [2], 174.91/44.76 174.91/44.76 [0 -&] [0] 174.91/44.76 [a](x0) = [1 1 ]x0 + [3] 174.91/44.76 orientation: 174.91/44.76 c#(c(x1)) = [2 1]x1 + [4] >= [0 1]x1 = b#(x1) 174.91/44.76 174.91/44.76 b#(a(x1)) = [2 2]x1 + [4] >= [0 1]x1 = b#(x1) 174.91/44.76 174.91/44.76 b#(a(x1)) = [2 2]x1 + [4] >= [2 2]x1 + [4] = c#(a(b(x1))) 174.91/44.76 174.91/44.76 [0 -&] [0] 174.91/44.76 a(x1) = [1 1 ]x1 + [3] >= x1 = x1 174.91/44.76 174.91/44.76 [1 1] [3] [1 1 ] [3] 174.91/44.76 b(a(x1)) = [1 1]x1 + [3] >= [-& 1 ]x1 + [3] = c(a(b(x1))) 174.91/44.76 174.91/44.76 [0 0] [2] 174.91/44.76 b(b(x1)) = [0 0]x1 + [2] >= x1 = x1 174.91/44.76 174.91/44.76 [1 0] [3] [-& 0 ] [1] 174.91/44.76 c(c(x1)) = [1 1]x1 + [3] >= [1 1 ]x1 + [3] = a(b(x1)) 174.91/44.76 problem: 174.91/44.76 DPs: 174.91/44.76 c#(c(x1)) -> b#(x1) 174.91/44.76 b#(a(x1)) -> c#(a(b(x1))) 174.91/44.76 TRS: 174.91/44.76 a(x1) -> x1 174.91/44.76 b(a(x1)) -> c(a(b(x1))) 174.91/44.76 b(b(x1)) -> x1 174.91/44.76 c(c(x1)) -> a(b(x1)) 174.91/44.76 Restore Modifier: 174.91/44.76 DPs: 174.91/44.76 c#(c(x1)) -> b#(x1) 174.91/44.76 b#(a(x1)) -> c#(a(b(x1))) 174.91/44.76 TRS: 174.91/44.76 a(x1) -> x1 174.91/44.76 b(a(x1)) -> c(a(b(x1))) 174.91/44.76 b(b(x1)) -> x1 174.91/44.76 c(c(x1)) -> a(b(x1)) 174.91/44.76 EDG Processor: 174.91/44.76 DPs: 174.91/44.76 c#(c(x1)) -> b#(x1) 174.91/44.76 b#(a(x1)) -> c#(a(b(x1))) 174.91/44.76 TRS: 174.91/44.76 a(x1) -> x1 174.91/44.76 b(a(x1)) -> c(a(b(x1))) 174.91/44.76 b(b(x1)) -> x1 174.91/44.76 c(c(x1)) -> a(b(x1)) 174.91/44.76 graph: 174.91/44.76 c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1))) 174.91/44.76 b#(a(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> b#(x1) 174.91/44.76 Arctic Interpretation Processor: 174.91/44.76 dimension: 2 174.91/44.76 usable rules: 174.91/44.76 a(x1) -> x1 174.91/44.76 b(a(x1)) -> c(a(b(x1))) 174.91/44.76 b(b(x1)) -> x1 174.91/44.76 c(c(x1)) -> a(b(x1)) 174.91/44.76 interpretation: 174.91/44.76 [c#](x0) = [1 2]x0 + [0], 174.91/44.76 174.91/44.76 [b#](x0) = [1 0]x0, 174.91/44.76 174.91/44.76 [0 2] [3] 174.91/44.76 [c](x0) = [1 3]x0 + [0], 174.91/44.76 174.91/44.76 [0 -&] [-&] 174.91/44.76 [b](x0) = [1 0 ]x0 + [1 ], 174.91/44.76 174.91/44.76 [3 2] [3] 174.91/44.76 [a](x0) = [0 0]x0 + [0] 174.91/44.76 orientation: 174.91/44.76 c#(c(x1)) = [3 5]x1 + [4] >= [1 0]x1 = b#(x1) 174.91/44.76 174.91/44.76 b#(a(x1)) = [4 3]x1 + [4] >= [4 3]x1 + [4] = c#(a(b(x1))) 174.91/44.76 174.91/44.76 [3 2] [3] 174.91/44.76 a(x1) = [0 0]x1 + [0] >= x1 = x1 174.91/44.76 174.91/44.76 [3 2] [3] [3 2] [3] 174.91/44.76 b(a(x1)) = [4 3]x1 + [4] >= [4 3]x1 + [4] = c(a(b(x1))) 174.91/44.76 174.91/44.76 [0 -&] [-&] 174.91/44.76 b(b(x1)) = [1 0 ]x1 + [1 ] >= x1 = x1 174.91/44.76 174.91/44.76 [3 5] [3] [3 2] [3] 174.91/44.76 c(c(x1)) = [4 6]x1 + [4] >= [1 0]x1 + [1] = a(b(x1)) 174.91/44.76 problem: 174.91/44.76 DPs: 174.91/44.76 b#(a(x1)) -> c#(a(b(x1))) 174.91/44.76 TRS: 174.91/44.76 a(x1) -> x1 174.91/44.76 b(a(x1)) -> c(a(b(x1))) 174.91/44.76 b(b(x1)) -> x1 174.91/44.76 c(c(x1)) -> a(b(x1)) 174.91/44.76 Restore Modifier: 174.91/44.76 DPs: 174.91/44.76 b#(a(x1)) -> c#(a(b(x1))) 174.91/44.76 TRS: 174.91/44.76 a(x1) -> x1 174.91/44.76 b(a(x1)) -> c(a(b(x1))) 174.91/44.76 b(b(x1)) -> x1 174.91/44.76 c(c(x1)) -> a(b(x1)) 174.91/44.76 EDG Processor: 174.91/44.76 DPs: 174.91/44.76 b#(a(x1)) -> c#(a(b(x1))) 174.91/44.76 TRS: 174.91/44.76 a(x1) -> x1 174.91/44.76 b(a(x1)) -> c(a(b(x1))) 174.91/44.76 b(b(x1)) -> x1 174.91/44.76 c(c(x1)) -> a(b(x1)) 174.91/44.76 graph: 174.91/44.76 174.91/44.76 SCC Processor: 174.91/44.76 #sccs: 0 174.91/44.76 #rules: 0 174.91/44.76 #arcs: 0/1 174.91/44.76 174.91/44.76 EOF