175.39/44.48 YES 175.39/44.49 175.39/44.49 Problem: 175.39/44.49 a(x1) -> x1 175.39/44.49 a(b(x1)) -> b(b(c(a(c(a(x1)))))) 175.39/44.49 b(x1) -> x1 175.39/44.49 c(c(x1)) -> x1 175.39/44.49 175.39/44.49 Proof: 175.39/44.49 DP Processor: 175.39/44.49 DPs: 175.39/44.49 a#(b(x1)) -> a#(x1) 175.39/44.49 a#(b(x1)) -> c#(a(x1)) 175.39/44.49 a#(b(x1)) -> a#(c(a(x1))) 175.39/44.49 a#(b(x1)) -> c#(a(c(a(x1)))) 175.39/44.49 a#(b(x1)) -> b#(c(a(c(a(x1))))) 175.39/44.49 a#(b(x1)) -> b#(b(c(a(c(a(x1)))))) 175.39/44.49 TRS: 175.39/44.49 a(x1) -> x1 175.39/44.49 a(b(x1)) -> b(b(c(a(c(a(x1)))))) 175.39/44.49 b(x1) -> x1 175.39/44.49 c(c(x1)) -> x1 175.39/44.49 TDG Processor: 175.39/44.49 DPs: 175.39/44.49 a#(b(x1)) -> a#(x1) 175.39/44.49 a#(b(x1)) -> c#(a(x1)) 175.39/44.49 a#(b(x1)) -> a#(c(a(x1))) 175.39/44.49 a#(b(x1)) -> c#(a(c(a(x1)))) 175.39/44.49 a#(b(x1)) -> b#(c(a(c(a(x1))))) 175.39/44.49 a#(b(x1)) -> b#(b(c(a(c(a(x1)))))) 175.39/44.49 TRS: 175.39/44.49 a(x1) -> x1 175.39/44.49 a(b(x1)) -> b(b(c(a(c(a(x1)))))) 175.39/44.49 b(x1) -> x1 175.39/44.49 c(c(x1)) -> x1 175.39/44.49 graph: 175.39/44.49 a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> b#(b(c(a(c(a(x1)))))) 175.39/44.49 a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> b#(c(a(c(a(x1))))) 175.39/44.49 a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> c#(a(c(a(x1)))) 175.39/44.49 a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> a#(c(a(x1))) 175.39/44.49 a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> c#(a(x1)) 175.39/44.49 a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> a#(x1) 175.39/44.49 a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(b(c(a(c(a(x1)))))) 175.39/44.49 a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(c(a(c(a(x1))))) 175.39/44.49 a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(a(c(a(x1)))) 175.39/44.49 a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(c(a(x1))) 175.39/44.49 a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(a(x1)) 175.39/44.49 a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1) 175.39/44.49 SCC Processor: 175.39/44.49 #sccs: 1 175.39/44.49 #rules: 2 175.39/44.49 #arcs: 12/36 175.39/44.49 DPs: 175.39/44.49 a#(b(x1)) -> a#(c(a(x1))) 175.39/44.49 a#(b(x1)) -> a#(x1) 175.39/44.49 TRS: 175.39/44.49 a(x1) -> x1 175.39/44.49 a(b(x1)) -> b(b(c(a(c(a(x1)))))) 175.39/44.49 b(x1) -> x1 175.39/44.49 c(c(x1)) -> x1 175.39/44.49 Arctic Interpretation Processor: 175.39/44.49 dimension: 2 175.39/44.49 usable rules: 175.39/44.49 a(x1) -> x1 175.39/44.49 a(b(x1)) -> b(b(c(a(c(a(x1)))))) 175.39/44.49 b(x1) -> x1 175.39/44.49 c(c(x1)) -> x1 175.39/44.49 interpretation: 175.39/44.49 [a#](x0) = [1 0]x0, 175.39/44.49 175.39/44.49 [-& 0 ] [0] 175.39/44.49 [c](x0) = [0 -&]x0 + [0], 175.39/44.49 175.39/44.49 [0 1 ] [3] 175.39/44.49 [b](x0) = [-& 0 ]x0 + [2], 175.39/44.49 175.39/44.49 [2 ] 175.39/44.49 [a](x0) = x0 + [-&] 175.39/44.49 orientation: 175.39/44.49 a#(b(x1)) = [1 2]x1 + [4] >= [0 1]x1 + [2] = a#(c(a(x1))) 175.39/44.49 175.39/44.49 a#(b(x1)) = [1 2]x1 + [4] >= [1 0]x1 = a#(x1) 175.39/44.49 175.39/44.49 [2 ] 175.39/44.49 a(x1) = x1 + [-&] >= x1 = x1 175.39/44.49 175.39/44.49 [0 1 ] [3] [0 1 ] [3] 175.39/44.49 a(b(x1)) = [-& 0 ]x1 + [2] >= [-& 0 ]x1 + [2] = b(b(c(a(c(a(x1)))))) 175.39/44.49 175.39/44.49 [0 1 ] [3] 175.39/44.49 b(x1) = [-& 0 ]x1 + [2] >= x1 = x1 175.39/44.49 175.39/44.49 [0] 175.39/44.49 c(c(x1)) = x1 + [0] >= x1 = x1 175.39/44.49 problem: 175.39/44.49 DPs: 175.39/44.49 a#(b(x1)) -> a#(x1) 175.39/44.49 TRS: 175.39/44.49 a(x1) -> x1 175.39/44.49 a(b(x1)) -> b(b(c(a(c(a(x1)))))) 175.39/44.49 b(x1) -> x1 175.39/44.49 c(c(x1)) -> x1 175.39/44.49 Restore Modifier: 175.39/44.49 DPs: 175.39/44.49 a#(b(x1)) -> a#(x1) 175.39/44.49 TRS: 175.39/44.49 a(x1) -> x1 175.39/44.49 a(b(x1)) -> b(b(c(a(c(a(x1)))))) 175.39/44.49 b(x1) -> x1 175.39/44.49 c(c(x1)) -> x1 175.39/44.49 EDG Processor: 175.39/44.49 DPs: 175.39/44.49 a#(b(x1)) -> a#(x1) 175.39/44.49 TRS: 175.39/44.49 a(x1) -> x1 175.39/44.49 a(b(x1)) -> b(b(c(a(c(a(x1)))))) 175.39/44.49 b(x1) -> x1 175.39/44.49 c(c(x1)) -> x1 175.39/44.49 graph: 175.39/44.49 a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1) 175.39/44.49 Usable Rule Processor: 175.39/44.49 DPs: 175.39/44.49 a#(b(x1)) -> a#(x1) 175.39/44.49 TRS: 175.39/44.49 175.39/44.49 Arctic Interpretation Processor: 175.39/44.49 dimension: 4 175.39/44.49 usable rules: 175.39/44.49 175.39/44.49 interpretation: 175.39/44.49 [a#](x0) = [0 -& -& -&]x0, 175.39/44.49 175.39/44.49 [1 0 0 0] [0] 175.39/44.49 [0 0 0 0] [0] 175.39/44.49 [b](x0) = [1 0 0 0]x0 + [0] 175.39/44.49 [0 0 0 0] [0] 175.39/44.49 orientation: 175.39/44.49 a#(b(x1)) = [1 0 0 0]x1 + [0] >= [0 -& -& -&]x1 = a#(x1) 175.39/44.49 problem: 175.39/44.49 DPs: 175.39/44.49 175.39/44.49 TRS: 175.39/44.49 175.39/44.49 Qed 175.39/44.49 EOF