/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: i(x,x) -> i(a(),b()) g(x,x) -> g(a(),b()) h(s(f(x))) -> h(f(x)) f(s(x)) -> s(s(f(h(s(x))))) f(g(s(x),y)) -> f(g(x,s(y))) h(g(x,s(y))) -> h(g(s(x),y)) h(i(x,y)) -> i(i(c(),h(h(y))),x) g(a(),g(x,g(b(),g(a(),g(x,y))))) -> g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) Proof: Matrix Interpretation Processor: dim=3 interpretation: [0] [c] = [0] [0], [1 0 0] [0] [h](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [0] [s](x0) = [0 0 0]x0 + [1] [1 0 0] [1], [1 1 1] [0] [f](x0) = [1 0 1]x0 + [1] [0 0 1] [1], [1 0 0] [1 0 0] [g](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [1 0 0] [0 0 0] , [0] [b] = [0] [0], [0] [a] = [0] [0], [1 0 0] [1 0 0] [0] [i](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0] orientation: [2 0 0] [0] [0] i(x,x) = [0 0 0]x + [1] >= [1] = i(a(),b()) [0 0 0] [0] [0] [2 0 0] [0] g(x,x) = [0 0 0]x >= [0] = g(a(),b()) [1 0 0] [0] [1 1 1] [0] [1 1 1] [0] h(s(f(x))) = [0 0 0]x + [1] >= [0 0 0]x + [1] = h(f(x)) [0 0 0] [0] [0 0 0] [0] [2 0 0] [2] [1 0 0] [1] f(s(x)) = [2 0 0]x + [2] >= [0 0 0]x + [1] = s(s(f(h(s(x))))) [1 0 0] [2] [1 0 0] [2] [2 0 0] [1 0 0] [0] [2 0 0] [1 0 0] [0] f(g(s(x),y)) = [2 0 0]x + [1 0 0]y + [1] >= [2 0 0]x + [1 0 0]y + [1] = f(g(x,s(y))) [1 0 0] [0 0 0] [1] [1 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] h(g(x,s(y))) = [0 0 0]x + [0 0 0]y + [1] >= [0 0 0]x + [0 0 0]y + [1] = h(g(s(x),y)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] h(i(x,y)) = [0 0 0]x + [0 0 0]y + [1] >= [0 0 0]x + [0 0 0]y + [1] = i(i(c(),h(h(y))),x) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [2 0 0] [1 0 0] [1 0 0] [1 0 0] g(a(),g(x,g(b(),g(a(),g(x,y))))) = [0 0 0]x + [0 0 0]y >= [0 0 0]x + [0 0 0]y = g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] problem: i(x,x) -> i(a(),b()) g(x,x) -> g(a(),b()) h(s(f(x))) -> h(f(x)) f(g(s(x),y)) -> f(g(x,s(y))) h(g(x,s(y))) -> h(g(s(x),y)) h(i(x,y)) -> i(i(c(),h(h(y))),x) g(a(),g(x,g(b(),g(a(),g(x,y))))) -> g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) Matrix Interpretation Processor: dim=1 interpretation: [c] = 0, [h](x0) = x0, [s](x0) = x0 + 1, [f](x0) = 4x0, [g](x0, x1) = x0 + x1, [b] = 0, [a] = 0, [i](x0, x1) = x0 + x1 orientation: i(x,x) = 2x >= 0 = i(a(),b()) g(x,x) = 2x >= 0 = g(a(),b()) h(s(f(x))) = 4x + 1 >= 4x = h(f(x)) f(g(s(x),y)) = 4x + 4y + 4 >= 4x + 4y + 4 = f(g(x,s(y))) h(g(x,s(y))) = x + y + 1 >= x + y + 1 = h(g(s(x),y)) h(i(x,y)) = x + y >= x + y = i(i(c(),h(h(y))),x) g(a(),g(x,g(b(),g(a(),g(x,y))))) = 2x + y >= x + y = g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) problem: i(x,x) -> i(a(),b()) g(x,x) -> g(a(),b()) f(g(s(x),y)) -> f(g(x,s(y))) h(g(x,s(y))) -> h(g(s(x),y)) h(i(x,y)) -> i(i(c(),h(h(y))),x) g(a(),g(x,g(b(),g(a(),g(x,y))))) -> g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) Matrix Interpretation Processor: dim=3 interpretation: [0] [c] = [0] [0], [1 1 0] [h](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [s](x0) = [0 1 1]x0 + [1] [0 0 0] [0], [1 0 0] [f](x0) = [0 0 0]x0 [1 0 0] , [1 1 0] [1 0 0] [g](x0, x1) = [0 0 1]x0 + [0 1 0]x1 [1 1 0] [0 0 0] , [0] [b] = [0] [0], [0] [a] = [0] [0], [1 1 1] [1 1 0] [i](x0, x1) = [0 0 1]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [2 2 1] [0] i(x,x) = [0 0 1]x >= [0] = i(a(),b()) [0 0 0] [0] [2 1 0] [0] g(x,x) = [0 1 1]x >= [0] = g(a(),b()) [1 1 0] [0] [1 1 1] [1 0 0] [2] [1 1 0] [1 0 0] [1] f(g(s(x),y)) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = f(g(x,s(y))) [1 1 1] [1 0 0] [2] [1 1 0] [1 0 0] [1] [1 1 1] [1 1 1] [2] [1 1 1] [1 1 0] [2] h(g(x,s(y))) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = h(g(s(x),y)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 2] [1 1 0] [1 1 0] [1 1 0] h(i(x,y)) = [0 0 0]x + [0 0 0]y >= [0 0 0]x + [0 0 0]y = i(i(c(),h(h(y))),x) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [2 2 0] [1 0 0] [1 1 0] [1 0 0] g(a(),g(x,g(b(),g(a(),g(x,y))))) = [0 0 2]x + [0 1 0]y >= [0 0 1]x + [0 1 0]y = g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] problem: i(x,x) -> i(a(),b()) g(x,x) -> g(a(),b()) h(g(x,s(y))) -> h(g(s(x),y)) h(i(x,y)) -> i(i(c(),h(h(y))),x) g(a(),g(x,g(b(),g(a(),g(x,y))))) -> g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) Matrix Interpretation Processor: dim=3 interpretation: [0] [c] = [0] [1], [1 0 0] [0] [h](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [0] [s](x0) = [0 0 0]x0 + [0] [1 0 1] [1], [1 1 0] [1 0 1] [g](x0, x1) = [0 1 1]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [b] = [0] [0], [0] [a] = [0] [0], [1 0 0] [1 0 0] [i](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 1] [0 0 0] orientation: [2 0 0] [0] i(x,x) = [0 0 0]x >= [0] = i(a(),b()) [0 0 1] [0] [2 1 1] [0] g(x,x) = [0 1 1]x >= [0] = g(a(),b()) [0 0 0] [0] [1 1 0] [2 0 1] [1] [1 0 0] [1 0 1] [0] h(g(x,s(y))) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = h(g(s(x),y)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] h(i(x,y)) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = i(i(c(),h(h(y))),x) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [2 2 0] [1 0 1] [1 1 0] [1 0 1] g(a(),g(x,g(b(),g(a(),g(x,y))))) = [0 0 0]x + [0 0 0]y >= [0 0 0]x + [0 0 0]y = g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] problem: i(x,x) -> i(a(),b()) g(x,x) -> g(a(),b()) h(i(x,y)) -> i(i(c(),h(h(y))),x) g(a(),g(x,g(b(),g(a(),g(x,y))))) -> g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) DP Processor: DPs: i#(x,x) -> i#(a(),b()) g#(x,x) -> g#(a(),b()) h#(i(x,y)) -> h#(y) h#(i(x,y)) -> h#(h(y)) h#(i(x,y)) -> i#(c(),h(h(y))) h#(i(x,y)) -> i#(i(c(),h(h(y))),x) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) TRS: i(x,x) -> i(a(),b()) g(x,x) -> g(a(),b()) h(i(x,y)) -> i(i(c(),h(h(y))),x) g(a(),g(x,g(b(),g(a(),g(x,y))))) -> g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) TDG Processor: DPs: i#(x,x) -> i#(a(),b()) g#(x,x) -> g#(a(),b()) h#(i(x,y)) -> h#(y) h#(i(x,y)) -> h#(h(y)) h#(i(x,y)) -> i#(c(),h(h(y))) h#(i(x,y)) -> i#(i(c(),h(h(y))),x) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) TRS: i(x,x) -> i(a(),b()) g(x,x) -> g(a(),b()) h(i(x,y)) -> i(i(c(),h(h(y))),x) g(a(),g(x,g(b(),g(a(),g(x,y))))) -> g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) graph: h#(i(x,y)) -> h#(h(y)) -> h#(i(x,y)) -> i#(i(c(),h(h(y))),x) h#(i(x,y)) -> h#(h(y)) -> h#(i(x,y)) -> i#(c(),h(h(y))) h#(i(x,y)) -> h#(h(y)) -> h#(i(x,y)) -> h#(h(y)) h#(i(x,y)) -> h#(h(y)) -> h#(i(x,y)) -> h#(y) h#(i(x,y)) -> h#(y) -> h#(i(x,y)) -> i#(i(c(),h(h(y))),x) h#(i(x,y)) -> h#(y) -> h#(i(x,y)) -> i#(c(),h(h(y))) h#(i(x,y)) -> h#(y) -> h#(i(x,y)) -> h#(h(y)) h#(i(x,y)) -> h#(y) -> h#(i(x,y)) -> h#(y) h#(i(x,y)) -> i#(c(),h(h(y))) -> i#(x,x) -> i#(a(),b()) h#(i(x,y)) -> i#(i(c(),h(h(y))),x) -> i#(x,x) -> i#(a(),b()) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) -> g#(x,x) -> g#(a(),b()) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) -> g#(x,x) -> g#(a(),b()) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) -> g#(x,x) -> g#(a(),b()) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) -> g#(x,x) -> g#(a(),b()) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) -> g#(x,x) -> g#(a(),b()) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) -> g#(x,x) -> g#(a(),b()) g#(x,x) -> g#(a(),b()) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) g#(x,x) -> g#(a(),b()) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) g#(x,x) -> g#(a(),b()) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) g#(x,x) -> g#(a(),b()) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) g#(x,x) -> g#(a(),b()) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) g#(x,x) -> g#(a(),b()) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) g#(x,x) -> g#(a(),b()) -> g#(x,x) -> g#(a(),b()) i#(x,x) -> i#(a(),b()) -> i#(x,x) -> i#(a(),b()) SCC Processor: #sccs: 3 #rules: 10 #arcs: 60/144 DPs: g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) g#(x,x) -> g#(a(),b()) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) TRS: i(x,x) -> i(a(),b()) g(x,x) -> g(a(),b()) h(i(x,y)) -> i(i(c(),h(h(y))),x) g(a(),g(x,g(b(),g(a(),g(x,y))))) -> g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) EDG Processor: DPs: g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) g#(x,x) -> g#(a(),b()) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) TRS: i(x,x) -> i(a(),b()) g(x,x) -> g(a(),b()) h(i(x,y)) -> i(i(c(),h(h(y))),x) g(a(),g(x,g(b(),g(a(),g(x,y))))) -> g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) graph: g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) -> g#(x,x) -> g#(a(),b()) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) -> g#(x,x) -> g#(a(),b()) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) -> g#(x,x) -> g#(a(),b()) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) -> g#(x,x) -> g#(a(),b()) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) -> g#(x,x) -> g#(a(),b()) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) -> g#(x,x) -> g#(a(),b()) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),y) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(b(),g(b(),y)) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(x,g(b(),g(b(),y)))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(x,g(b(),g(b(),y))))) g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) -> g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) SCC Processor: #sccs: 1 #rules: 1 #arcs: 12/49 DPs: g#(a(),g(x,g(b(),g(a(),g(x,y))))) -> g#(x,g(b(),g(b(),y))) TRS: i(x,x) -> i(a(),b()) g(x,x) -> g(a(),b()) h(i(x,y)) -> i(i(c(),h(h(y))),x) g(a(),g(x,g(b(),g(a(),g(x,y))))) -> g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {1} transitions: f110() -> 2* g{#,0}(3,5) -> 1* g{#,0}(3,9) -> 1* g{#,0}(2,5) -> 1* g{#,0}(2,9) -> 1* g0(3,9) -> 5* g0(3,2) -> 4* g0(3,4) -> 5* g0(6,3) -> 9*,4,5 b0() -> 3* a0() -> 6* problem: DPs: TRS: i(x,x) -> i(a(),b()) g(x,x) -> g(a(),b()) h(i(x,y)) -> i(i(c(),h(h(y))),x) g(a(),g(x,g(b(),g(a(),g(x,y))))) -> g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) Qed DPs: h#(i(x,y)) -> h#(h(y)) h#(i(x,y)) -> h#(y) TRS: i(x,x) -> i(a(),b()) g(x,x) -> g(a(),b()) h(i(x,y)) -> i(i(c(),h(h(y))),x) g(a(),g(x,g(b(),g(a(),g(x,y))))) -> g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) Bounds Processor: bound: 1 enrichment: match-dp automaton: final states: {16,4,1} transitions: f170() -> 2* h{#,0}(20) -> 16* h{#,0}(17) -> 16* h{#,0}(3) -> 16*,4,1 h0(20) -> 5* h0(17) -> 5* h0(3) -> 5* i0(17,7) -> 5* i0(7,7) -> 5* i0(17,17) -> 5* i0(7,17) -> 5* i0(6,5) -> 7* i0(6,17) -> 7* i0(17,2) -> 17* i0(7,2) -> 17*,5,7,3 c0() -> 6* h{#,1}(20) -> 16* h{#,1}(2) -> 4,1,16* h{#,1}(18) -> 16* h1(2) -> 20*,3,18 b0() -> 2* a0() -> 7* 1 -> 4* problem: DPs: TRS: i(x,x) -> i(a(),b()) g(x,x) -> g(a(),b()) h(i(x,y)) -> i(i(c(),h(h(y))),x) g(a(),g(x,g(b(),g(a(),g(x,y))))) -> g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) Qed DPs: i#(x,x) -> i#(a(),b()) TRS: i(x,x) -> i(a(),b()) g(x,x) -> g(a(),b()) h(i(x,y)) -> i(i(c(),h(h(y))),x) g(a(),g(x,g(b(),g(a(),g(x,y))))) -> g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) EDG Processor: DPs: i#(x,x) -> i#(a(),b()) TRS: i(x,x) -> i(a(),b()) g(x,x) -> g(a(),b()) h(i(x,y)) -> i(i(c(),h(h(y))),x) g(a(),g(x,g(b(),g(a(),g(x,y))))) -> g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y)))))) graph: SCC Processor: #sccs: 0 #rules: 0 #arcs: 0/1