/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: a(b(x1)) -> b(c(a(x1))) b(c(x1)) -> c(b(b(x1))) a(c(x1)) -> c(a(b(x1))) a(a(x1)) -> a(d(d(d(x1)))) d(a(x1)) -> d(d(c(x1))) a(d(d(c(x1)))) -> a(a(a(d(x1)))) e(e(f(f(x1)))) -> f(f(f(e(e(x1))))) e(x1) -> a(x1) b(d(x1)) -> d(d(x1)) Proof: Matrix Interpretation Processor: dim=1 interpretation: [e](x0) = 4x0 + 4, [f](x0) = x0, [d](x0) = x0, [c](x0) = x0, [a](x0) = x0, [b](x0) = x0 orientation: a(b(x1)) = x1 >= x1 = b(c(a(x1))) b(c(x1)) = x1 >= x1 = c(b(b(x1))) a(c(x1)) = x1 >= x1 = c(a(b(x1))) a(a(x1)) = x1 >= x1 = a(d(d(d(x1)))) d(a(x1)) = x1 >= x1 = d(d(c(x1))) a(d(d(c(x1)))) = x1 >= x1 = a(a(a(d(x1)))) e(e(f(f(x1)))) = 16x1 + 20 >= 16x1 + 20 = f(f(f(e(e(x1))))) e(x1) = 4x1 + 4 >= x1 = a(x1) b(d(x1)) = x1 >= x1 = d(d(x1)) problem: a(b(x1)) -> b(c(a(x1))) b(c(x1)) -> c(b(b(x1))) a(c(x1)) -> c(a(b(x1))) a(a(x1)) -> a(d(d(d(x1)))) d(a(x1)) -> d(d(c(x1))) a(d(d(c(x1)))) -> a(a(a(d(x1)))) e(e(f(f(x1)))) -> f(f(f(e(e(x1))))) b(d(x1)) -> d(d(x1)) Matrix Interpretation Processor: dim=1 interpretation: [e](x0) = 2x0 + 4, [f](x0) = x0 + 1, [d](x0) = x0, [c](x0) = x0, [a](x0) = x0, [b](x0) = x0 orientation: a(b(x1)) = x1 >= x1 = b(c(a(x1))) b(c(x1)) = x1 >= x1 = c(b(b(x1))) a(c(x1)) = x1 >= x1 = c(a(b(x1))) a(a(x1)) = x1 >= x1 = a(d(d(d(x1)))) d(a(x1)) = x1 >= x1 = d(d(c(x1))) a(d(d(c(x1)))) = x1 >= x1 = a(a(a(d(x1)))) e(e(f(f(x1)))) = 4x1 + 20 >= 4x1 + 15 = f(f(f(e(e(x1))))) b(d(x1)) = x1 >= x1 = d(d(x1)) problem: a(b(x1)) -> b(c(a(x1))) b(c(x1)) -> c(b(b(x1))) a(c(x1)) -> c(a(b(x1))) a(a(x1)) -> a(d(d(d(x1)))) d(a(x1)) -> d(d(c(x1))) a(d(d(c(x1)))) -> a(a(a(d(x1)))) b(d(x1)) -> d(d(x1)) String Reversal Processor: b(a(x1)) -> a(c(b(x1))) c(b(x1)) -> b(b(c(x1))) c(a(x1)) -> b(a(c(x1))) a(a(x1)) -> d(d(d(a(x1)))) a(d(x1)) -> c(d(d(x1))) c(d(d(a(x1)))) -> d(a(a(a(x1)))) d(b(x1)) -> d(d(x1)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [d](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [c](x0) = [0 1 1]x0 + [1] [0 1 1] [0], [1 0 0] [0] [a](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [0] [b](x0) = x0 + [1] [1] orientation: [1 0 0] [0] [1 0 0] [0] b(a(x1)) = [0 0 0]x1 + [2] >= [0 0 0]x1 + [1] = a(c(b(x1))) [0 0 0] [1] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] c(b(x1)) = [0 1 1]x1 + [3] >= [0 1 1]x1 + [3] = b(b(c(x1))) [0 1 1] [2] [0 1 1] [2] [1 0 0] [0] [1 0 0] [0] c(a(x1)) = [0 0 0]x1 + [2] >= [0 0 0]x1 + [2] = b(a(c(x1))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] a(a(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 = d(d(d(a(x1)))) [0 0 0] [0] [0 0 0] [1 0 1] [0] [1 0 1] [0] a(d(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = c(d(d(x1))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] c(d(d(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = d(a(a(a(x1)))) [0 0 0] [0] [0 0 0] [1 0 1] [1] [1 0 1] d(b(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 = d(d(x1)) [0 0 0] [0] [0 0 0] problem: b(a(x1)) -> a(c(b(x1))) c(b(x1)) -> b(b(c(x1))) c(a(x1)) -> b(a(c(x1))) a(a(x1)) -> d(d(d(a(x1)))) a(d(x1)) -> c(d(d(x1))) c(d(d(a(x1)))) -> d(a(a(a(x1)))) String Reversal Processor: a(b(x1)) -> b(c(a(x1))) b(c(x1)) -> c(b(b(x1))) a(c(x1)) -> c(a(b(x1))) a(a(x1)) -> a(d(d(d(x1)))) d(a(x1)) -> d(d(c(x1))) a(d(d(c(x1)))) -> a(a(a(d(x1)))) DP Processor: DPs: a#(b(x1)) -> a#(x1) a#(b(x1)) -> b#(c(a(x1))) b#(c(x1)) -> b#(x1) b#(c(x1)) -> b#(b(x1)) a#(c(x1)) -> b#(x1) a#(c(x1)) -> a#(b(x1)) a#(a(x1)) -> d#(x1) a#(a(x1)) -> d#(d(x1)) a#(a(x1)) -> d#(d(d(x1))) a#(a(x1)) -> a#(d(d(d(x1)))) d#(a(x1)) -> d#(c(x1)) d#(a(x1)) -> d#(d(c(x1))) a#(d(d(c(x1)))) -> d#(x1) a#(d(d(c(x1)))) -> a#(d(x1)) a#(d(d(c(x1)))) -> a#(a(d(x1))) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) TRS: a(b(x1)) -> b(c(a(x1))) b(c(x1)) -> c(b(b(x1))) a(c(x1)) -> c(a(b(x1))) a(a(x1)) -> a(d(d(d(x1)))) d(a(x1)) -> d(d(c(x1))) a(d(d(c(x1)))) -> a(a(a(d(x1)))) TDG Processor: DPs: a#(b(x1)) -> a#(x1) a#(b(x1)) -> b#(c(a(x1))) b#(c(x1)) -> b#(x1) b#(c(x1)) -> b#(b(x1)) a#(c(x1)) -> b#(x1) a#(c(x1)) -> a#(b(x1)) a#(a(x1)) -> d#(x1) a#(a(x1)) -> d#(d(x1)) a#(a(x1)) -> d#(d(d(x1))) a#(a(x1)) -> a#(d(d(d(x1)))) d#(a(x1)) -> d#(c(x1)) d#(a(x1)) -> d#(d(c(x1))) a#(d(d(c(x1)))) -> d#(x1) a#(d(d(c(x1)))) -> a#(d(x1)) a#(d(d(c(x1)))) -> a#(a(d(x1))) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) TRS: a(b(x1)) -> b(c(a(x1))) b(c(x1)) -> c(b(b(x1))) a(c(x1)) -> c(a(b(x1))) a(a(x1)) -> a(d(d(d(x1)))) d(a(x1)) -> d(d(c(x1))) a(d(d(c(x1)))) -> a(a(a(d(x1)))) graph: d#(a(x1)) -> d#(d(c(x1))) -> d#(a(x1)) -> d#(d(c(x1))) d#(a(x1)) -> d#(d(c(x1))) -> d#(a(x1)) -> d#(c(x1)) d#(a(x1)) -> d#(c(x1)) -> d#(a(x1)) -> d#(d(c(x1))) d#(a(x1)) -> d#(c(x1)) -> d#(a(x1)) -> d#(c(x1)) b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(x1) b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1)) b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1) a#(d(d(c(x1)))) -> d#(x1) -> d#(a(x1)) -> d#(d(c(x1))) a#(d(d(c(x1)))) -> d#(x1) -> d#(a(x1)) -> d#(c(x1)) a#(d(d(c(x1)))) -> a#(d(x1)) -> a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) a#(d(d(c(x1)))) -> a#(d(x1)) -> a#(d(d(c(x1)))) -> a#(a(d(x1))) a#(d(d(c(x1)))) -> a#(d(x1)) -> a#(d(d(c(x1)))) -> a#(d(x1)) a#(d(d(c(x1)))) -> a#(d(x1)) -> a#(d(d(c(x1)))) -> d#(x1) a#(d(d(c(x1)))) -> a#(d(x1)) -> a#(a(x1)) -> a#(d(d(d(x1)))) a#(d(d(c(x1)))) -> a#(d(x1)) -> a#(a(x1)) -> d#(d(d(x1))) a#(d(d(c(x1)))) -> a#(d(x1)) -> a#(a(x1)) -> d#(d(x1)) a#(d(d(c(x1)))) -> a#(d(x1)) -> a#(a(x1)) -> d#(x1) a#(d(d(c(x1)))) -> a#(d(x1)) -> a#(c(x1)) -> a#(b(x1)) a#(d(d(c(x1)))) -> a#(d(x1)) -> a#(c(x1)) -> b#(x1) a#(d(d(c(x1)))) -> a#(d(x1)) -> a#(b(x1)) -> b#(c(a(x1))) a#(d(d(c(x1)))) -> a#(d(x1)) -> a#(b(x1)) -> a#(x1) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(d(d(c(x1)))) -> a#(a(d(x1))) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(d(d(c(x1)))) -> a#(d(x1)) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(d(d(c(x1)))) -> d#(x1) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(a(x1)) -> a#(d(d(d(x1)))) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(a(x1)) -> d#(d(d(x1))) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(a(x1)) -> d#(d(x1)) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(a(x1)) -> d#(x1) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(c(x1)) -> a#(b(x1)) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(c(x1)) -> b#(x1) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(b(x1)) -> b#(c(a(x1))) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(b(x1)) -> a#(x1) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(d(d(c(x1)))) -> a#(a(d(x1))) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(d(d(c(x1)))) -> a#(d(x1)) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(d(d(c(x1)))) -> d#(x1) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(a(x1)) -> a#(d(d(d(x1)))) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(a(x1)) -> d#(d(d(x1))) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(a(x1)) -> d#(d(x1)) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(a(x1)) -> d#(x1) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(c(x1)) -> a#(b(x1)) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(c(x1)) -> b#(x1) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(b(x1)) -> b#(c(a(x1))) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(b(x1)) -> a#(x1) a#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1)) a#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1) a#(c(x1)) -> a#(b(x1)) -> a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) a#(c(x1)) -> a#(b(x1)) -> a#(d(d(c(x1)))) -> a#(a(d(x1))) a#(c(x1)) -> a#(b(x1)) -> a#(d(d(c(x1)))) -> a#(d(x1)) a#(c(x1)) -> a#(b(x1)) -> a#(d(d(c(x1)))) -> d#(x1) a#(c(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(d(d(d(x1)))) a#(c(x1)) -> a#(b(x1)) -> a#(a(x1)) -> d#(d(d(x1))) a#(c(x1)) -> a#(b(x1)) -> a#(a(x1)) -> d#(d(x1)) a#(c(x1)) -> a#(b(x1)) -> a#(a(x1)) -> d#(x1) a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> b#(x1) a#(c(x1)) -> a#(b(x1)) -> a#(b(x1)) -> b#(c(a(x1))) a#(c(x1)) -> a#(b(x1)) -> a#(b(x1)) -> a#(x1) a#(a(x1)) -> d#(d(d(x1))) -> d#(a(x1)) -> d#(d(c(x1))) a#(a(x1)) -> d#(d(d(x1))) -> d#(a(x1)) -> d#(c(x1)) a#(a(x1)) -> d#(d(x1)) -> d#(a(x1)) -> d#(d(c(x1))) a#(a(x1)) -> d#(d(x1)) -> d#(a(x1)) -> d#(c(x1)) a#(a(x1)) -> d#(x1) -> d#(a(x1)) -> d#(d(c(x1))) a#(a(x1)) -> d#(x1) -> d#(a(x1)) -> d#(c(x1)) a#(a(x1)) -> a#(d(d(d(x1)))) -> a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) a#(a(x1)) -> a#(d(d(d(x1)))) -> a#(d(d(c(x1)))) -> a#(a(d(x1))) a#(a(x1)) -> a#(d(d(d(x1)))) -> a#(d(d(c(x1)))) -> a#(d(x1)) a#(a(x1)) -> a#(d(d(d(x1)))) -> a#(d(d(c(x1)))) -> d#(x1) a#(a(x1)) -> a#(d(d(d(x1)))) -> a#(a(x1)) -> a#(d(d(d(x1)))) a#(a(x1)) -> a#(d(d(d(x1)))) -> a#(a(x1)) -> d#(d(d(x1))) a#(a(x1)) -> a#(d(d(d(x1)))) -> a#(a(x1)) -> d#(d(x1)) a#(a(x1)) -> a#(d(d(d(x1)))) -> a#(a(x1)) -> d#(x1) a#(a(x1)) -> a#(d(d(d(x1)))) -> a#(c(x1)) -> a#(b(x1)) a#(a(x1)) -> a#(d(d(d(x1)))) -> a#(c(x1)) -> b#(x1) a#(a(x1)) -> a#(d(d(d(x1)))) -> a#(b(x1)) -> b#(c(a(x1))) a#(a(x1)) -> a#(d(d(d(x1)))) -> a#(b(x1)) -> a#(x1) a#(b(x1)) -> b#(c(a(x1))) -> b#(c(x1)) -> b#(b(x1)) a#(b(x1)) -> b#(c(a(x1))) -> b#(c(x1)) -> b#(x1) a#(b(x1)) -> a#(x1) -> a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) a#(b(x1)) -> a#(x1) -> a#(d(d(c(x1)))) -> a#(a(d(x1))) a#(b(x1)) -> a#(x1) -> a#(d(d(c(x1)))) -> a#(d(x1)) a#(b(x1)) -> a#(x1) -> a#(d(d(c(x1)))) -> d#(x1) a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(d(d(d(x1)))) a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> d#(d(d(x1))) a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> d#(d(x1)) a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> d#(x1) a#(b(x1)) -> a#(x1) -> a#(c(x1)) -> a#(b(x1)) a#(b(x1)) -> a#(x1) -> a#(c(x1)) -> b#(x1) a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(c(a(x1))) a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1) EDG Processor: DPs: a#(b(x1)) -> a#(x1) a#(b(x1)) -> b#(c(a(x1))) b#(c(x1)) -> b#(x1) b#(c(x1)) -> b#(b(x1)) a#(c(x1)) -> b#(x1) a#(c(x1)) -> a#(b(x1)) a#(a(x1)) -> d#(x1) a#(a(x1)) -> d#(d(x1)) a#(a(x1)) -> d#(d(d(x1))) a#(a(x1)) -> a#(d(d(d(x1)))) d#(a(x1)) -> d#(c(x1)) d#(a(x1)) -> d#(d(c(x1))) a#(d(d(c(x1)))) -> d#(x1) a#(d(d(c(x1)))) -> a#(d(x1)) a#(d(d(c(x1)))) -> a#(a(d(x1))) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) TRS: a(b(x1)) -> b(c(a(x1))) b(c(x1)) -> c(b(b(x1))) a(c(x1)) -> c(a(b(x1))) a(a(x1)) -> a(d(d(d(x1)))) d(a(x1)) -> d(d(c(x1))) a(d(d(c(x1)))) -> a(a(a(d(x1)))) graph: b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(x1) b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1) b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1)) a#(d(d(c(x1)))) -> d#(x1) -> d#(a(x1)) -> d#(c(x1)) a#(d(d(c(x1)))) -> d#(x1) -> d#(a(x1)) -> d#(d(c(x1))) a#(d(d(c(x1)))) -> a#(d(x1)) -> a#(d(d(c(x1)))) -> d#(x1) a#(d(d(c(x1)))) -> a#(d(x1)) -> a#(d(d(c(x1)))) -> a#(d(x1)) a#(d(d(c(x1)))) -> a#(d(x1)) -> a#(d(d(c(x1)))) -> a#(a(d(x1))) a#(d(d(c(x1)))) -> a#(d(x1)) -> a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(b(x1)) -> a#(x1) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(b(x1)) -> b#(c(a(x1))) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(c(x1)) -> b#(x1) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(c(x1)) -> a#(b(x1)) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(a(x1)) -> d#(x1) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(a(x1)) -> d#(d(x1)) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(a(x1)) -> d#(d(d(x1))) a#(d(d(c(x1)))) -> a#(a(d(x1))) -> a#(a(x1)) -> a#(d(d(d(x1)))) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(b(x1)) -> a#(x1) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(b(x1)) -> b#(c(a(x1))) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(c(x1)) -> b#(x1) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(c(x1)) -> a#(b(x1)) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(a(x1)) -> d#(x1) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(a(x1)) -> d#(d(x1)) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(a(x1)) -> d#(d(d(x1))) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) -> a#(a(x1)) -> a#(d(d(d(x1)))) a#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1) a#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1)) a#(c(x1)) -> a#(b(x1)) -> a#(b(x1)) -> a#(x1) a#(c(x1)) -> a#(b(x1)) -> a#(b(x1)) -> b#(c(a(x1))) a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> b#(x1) a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) a#(a(x1)) -> d#(x1) -> d#(a(x1)) -> d#(c(x1)) a#(a(x1)) -> d#(x1) -> d#(a(x1)) -> d#(d(c(x1))) a#(b(x1)) -> b#(c(a(x1))) -> b#(c(x1)) -> b#(x1) a#(b(x1)) -> b#(c(a(x1))) -> b#(c(x1)) -> b#(b(x1)) a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1) a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(c(a(x1))) a#(b(x1)) -> a#(x1) -> a#(c(x1)) -> b#(x1) a#(b(x1)) -> a#(x1) -> a#(c(x1)) -> a#(b(x1)) a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> d#(x1) a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> d#(d(x1)) a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> d#(d(d(x1))) a#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(d(d(d(x1)))) a#(b(x1)) -> a#(x1) -> a#(d(d(c(x1)))) -> d#(x1) a#(b(x1)) -> a#(x1) -> a#(d(d(c(x1)))) -> a#(d(x1)) a#(b(x1)) -> a#(x1) -> a#(d(d(c(x1)))) -> a#(a(d(x1))) a#(b(x1)) -> a#(x1) -> a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) SCC Processor: #sccs: 2 #rules: 7 #arcs: 48/256 DPs: a#(d(d(c(x1)))) -> a#(d(x1)) a#(d(d(c(x1)))) -> a#(a(a(d(x1)))) a#(c(x1)) -> a#(b(x1)) a#(b(x1)) -> a#(x1) a#(d(d(c(x1)))) -> a#(a(d(x1))) TRS: a(b(x1)) -> b(c(a(x1))) b(c(x1)) -> c(b(b(x1))) a(c(x1)) -> c(a(b(x1))) a(a(x1)) -> a(d(d(d(x1)))) d(a(x1)) -> d(d(c(x1))) a(d(d(c(x1)))) -> a(a(a(d(x1)))) Arctic Interpretation Processor: dimension: 1 usable rules: a(b(x1)) -> b(c(a(x1))) b(c(x1)) -> c(b(b(x1))) a(c(x1)) -> c(a(b(x1))) a(a(x1)) -> a(d(d(d(x1)))) d(a(x1)) -> d(d(c(x1))) a(d(d(c(x1)))) -> a(a(a(d(x1)))) interpretation: [a#](x0) = x0, [d](x0) = 9, [c](x0) = x0, [a](x0) = 8, [b](x0) = x0 orientation: a#(d(d(c(x1)))) = 9 >= 9 = a#(d(x1)) a#(d(d(c(x1)))) = 9 >= 8 = a#(a(a(d(x1)))) a#(c(x1)) = x1 >= x1 = a#(b(x1)) a#(b(x1)) = x1 >= x1 = a#(x1) a#(d(d(c(x1)))) = 9 >= 8 = a#(a(d(x1))) a(b(x1)) = 8 >= 8 = b(c(a(x1))) b(c(x1)) = x1 >= x1 = c(b(b(x1))) a(c(x1)) = 8 >= 8 = c(a(b(x1))) a(a(x1)) = 8 >= 8 = a(d(d(d(x1)))) d(a(x1)) = 9 >= 9 = d(d(c(x1))) a(d(d(c(x1)))) = 8 >= 8 = a(a(a(d(x1)))) problem: DPs: a#(d(d(c(x1)))) -> a#(d(x1)) a#(c(x1)) -> a#(b(x1)) a#(b(x1)) -> a#(x1) TRS: a(b(x1)) -> b(c(a(x1))) b(c(x1)) -> c(b(b(x1))) a(c(x1)) -> c(a(b(x1))) a(a(x1)) -> a(d(d(d(x1)))) d(a(x1)) -> d(d(c(x1))) a(d(d(c(x1)))) -> a(a(a(d(x1)))) Restore Modifier: DPs: a#(d(d(c(x1)))) -> a#(d(x1)) a#(c(x1)) -> a#(b(x1)) a#(b(x1)) -> a#(x1) TRS: a(b(x1)) -> b(c(a(x1))) b(c(x1)) -> c(b(b(x1))) a(c(x1)) -> c(a(b(x1))) a(a(x1)) -> a(d(d(d(x1)))) d(a(x1)) -> d(d(c(x1))) a(d(d(c(x1)))) -> a(a(a(d(x1)))) EDG Processor: DPs: a#(d(d(c(x1)))) -> a#(d(x1)) a#(c(x1)) -> a#(b(x1)) a#(b(x1)) -> a#(x1) TRS: a(b(x1)) -> b(c(a(x1))) b(c(x1)) -> c(b(b(x1))) a(c(x1)) -> c(a(b(x1))) a(a(x1)) -> a(d(d(d(x1)))) d(a(x1)) -> d(d(c(x1))) a(d(d(c(x1)))) -> a(a(a(d(x1)))) graph: a#(d(d(c(x1)))) -> a#(d(x1)) -> a#(d(d(c(x1)))) -> a#(d(x1)) a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) a#(c(x1)) -> a#(b(x1)) -> a#(b(x1)) -> a#(x1) a#(b(x1)) -> a#(x1) -> a#(d(d(c(x1)))) -> a#(d(x1)) a#(b(x1)) -> a#(x1) -> a#(c(x1)) -> a#(b(x1)) a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1) SCC Processor: #sccs: 2 #rules: 3 #arcs: 6/9 DPs: a#(c(x1)) -> a#(b(x1)) a#(b(x1)) -> a#(x1) TRS: a(b(x1)) -> b(c(a(x1))) b(c(x1)) -> c(b(b(x1))) a(c(x1)) -> c(a(b(x1))) a(a(x1)) -> a(d(d(d(x1)))) d(a(x1)) -> d(d(c(x1))) a(d(d(c(x1)))) -> a(a(a(d(x1)))) Usable Rule Processor: DPs: a#(c(x1)) -> a#(b(x1)) a#(b(x1)) -> a#(x1) TRS: b(c(x1)) -> c(b(b(x1))) Arctic Interpretation Processor: dimension: 1 usable rules: b(c(x1)) -> c(b(b(x1))) interpretation: [a#](x0) = x0 + 0, [c](x0) = 1x0 + 14, [b](x0) = x0 orientation: a#(c(x1)) = 1x1 + 14 >= x1 + 0 = a#(b(x1)) a#(b(x1)) = x1 + 0 >= x1 + 0 = a#(x1) b(c(x1)) = 1x1 + 14 >= 1x1 + 14 = c(b(b(x1))) problem: DPs: a#(b(x1)) -> a#(x1) TRS: b(c(x1)) -> c(b(b(x1))) Restore Modifier: DPs: a#(b(x1)) -> a#(x1) TRS: a(b(x1)) -> b(c(a(x1))) b(c(x1)) -> c(b(b(x1))) a(c(x1)) -> c(a(b(x1))) a(a(x1)) -> a(d(d(d(x1)))) d(a(x1)) -> d(d(c(x1))) a(d(d(c(x1)))) -> a(a(a(d(x1)))) EDG Processor: DPs: a#(b(x1)) -> a#(x1) TRS: a(b(x1)) -> b(c(a(x1))) b(c(x1)) -> c(b(b(x1))) a(c(x1)) -> c(a(b(x1))) a(a(x1)) -> a(d(d(d(x1)))) d(a(x1)) -> d(d(c(x1))) a(d(d(c(x1)))) -> a(a(a(d(x1)))) graph: a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1) Usable Rule Processor: DPs: a#(b(x1)) -> a#(x1) TRS: Arctic Interpretation Processor: dimension: 4 usable rules: interpretation: [a#](x0) = [0 -& -& -&]x0, [1 0 0 0] [0] [0 0 0 0] [0] [b](x0) = [1 0 0 0]x0 + [0] [0 0 0 0] [0] orientation: a#(b(x1)) = [1 0 0 0]x1 + [0] >= [0 -& -& -&]x1 = a#(x1) problem: DPs: TRS: Qed DPs: a#(d(d(c(x1)))) -> a#(d(x1)) TRS: a(b(x1)) -> b(c(a(x1))) b(c(x1)) -> c(b(b(x1))) a(c(x1)) -> c(a(b(x1))) a(a(x1)) -> a(d(d(d(x1)))) d(a(x1)) -> d(d(c(x1))) a(d(d(c(x1)))) -> a(a(a(d(x1)))) Usable Rule Processor: DPs: a#(d(d(c(x1)))) -> a#(d(x1)) TRS: d(a(x1)) -> d(d(c(x1))) Arctic Interpretation Processor: dimension: 1 usable rules: d(a(x1)) -> d(d(c(x1))) interpretation: [a#](x0) = x0, [d](x0) = x0, [c](x0) = 5x0, [a](x0) = 5x0 + 13 orientation: a#(d(d(c(x1)))) = 5x1 >= x1 = a#(d(x1)) d(a(x1)) = 5x1 + 13 >= 5x1 = d(d(c(x1))) problem: DPs: TRS: d(a(x1)) -> d(d(c(x1))) Qed DPs: b#(c(x1)) -> b#(b(x1)) b#(c(x1)) -> b#(x1) TRS: a(b(x1)) -> b(c(a(x1))) b(c(x1)) -> c(b(b(x1))) a(c(x1)) -> c(a(b(x1))) a(a(x1)) -> a(d(d(d(x1)))) d(a(x1)) -> d(d(c(x1))) a(d(d(c(x1)))) -> a(a(a(d(x1)))) Usable Rule Processor: DPs: b#(c(x1)) -> b#(b(x1)) b#(c(x1)) -> b#(x1) TRS: b(c(x1)) -> c(b(b(x1))) Arctic Interpretation Processor: dimension: 1 usable rules: b(c(x1)) -> c(b(b(x1))) interpretation: [b#](x0) = 3x0, [c](x0) = 1x0, [b](x0) = x0 orientation: b#(c(x1)) = 4x1 >= 3x1 = b#(b(x1)) b#(c(x1)) = 4x1 >= 3x1 = b#(x1) b(c(x1)) = 1x1 >= 1x1 = c(b(b(x1))) problem: DPs: TRS: b(c(x1)) -> c(b(b(x1))) Qed