MAYBE TRS: {f(x, f(a(), y)) -> f(a(), f(f(a(), h(f(a(), x))), y))} DP: Strict: {f#(x, f(a(), y)) -> f#(f(a(), h(f(a(), x))), y), f#(x, f(a(), y)) -> f#(a(), x), f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y)), f#(x, f(a(), y)) -> f#(a(), h(f(a(), x)))} Weak: {f(x, f(a(), y)) -> f(a(), f(f(a(), h(f(a(), x))), y))} EDG: {(f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y)), f#(x, f(a(), y)) -> f#(a(), h(f(a(), x)))) (f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y)), f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y))) (f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y)), f#(x, f(a(), y)) -> f#(a(), x)) (f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y)), f#(x, f(a(), y)) -> f#(f(a(), h(f(a(), x))), y)) (f#(x, f(a(), y)) -> f#(a(), x), f#(x, f(a(), y)) -> f#(f(a(), h(f(a(), x))), y)) (f#(x, f(a(), y)) -> f#(a(), x), f#(x, f(a(), y)) -> f#(a(), x)) (f#(x, f(a(), y)) -> f#(a(), x), f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y))) (f#(x, f(a(), y)) -> f#(a(), x), f#(x, f(a(), y)) -> f#(a(), h(f(a(), x)))) (f#(x, f(a(), y)) -> f#(f(a(), h(f(a(), x))), y), f#(x, f(a(), y)) -> f#(f(a(), h(f(a(), x))), y)) (f#(x, f(a(), y)) -> f#(f(a(), h(f(a(), x))), y), f#(x, f(a(), y)) -> f#(a(), x)) (f#(x, f(a(), y)) -> f#(f(a(), h(f(a(), x))), y), f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y))) (f#(x, f(a(), y)) -> f#(f(a(), h(f(a(), x))), y), f#(x, f(a(), y)) -> f#(a(), h(f(a(), x))))} SCCS: Scc: {f#(x, f(a(), y)) -> f#(f(a(), h(f(a(), x))), y), f#(x, f(a(), y)) -> f#(a(), x), f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y))} SCC: Strict: {f#(x, f(a(), y)) -> f#(f(a(), h(f(a(), x))), y), f#(x, f(a(), y)) -> f#(a(), x), f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y))} Weak: {f(x, f(a(), y)) -> f(a(), f(f(a(), h(f(a(), x))), y))} POLY: Argument Filtering: pi(h) = [], pi(a) = [], pi(f#) = [0,1], pi(f) = [1] Usable Rules: {} Interpretation: [f#](x0, x1) = x0 + x1, [f](x0) = x0 + 1, [h] = 0, [a] = 0 Strict: {f#(x, f(a(), y)) -> f#(f(a(), h(f(a(), x))), y), f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y))} Weak: {f(x, f(a(), y)) -> f(a(), f(f(a(), h(f(a(), x))), y))} EDG: {(f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y)), f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y))) (f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y)), f#(x, f(a(), y)) -> f#(f(a(), h(f(a(), x))), y)) (f#(x, f(a(), y)) -> f#(f(a(), h(f(a(), x))), y), f#(x, f(a(), y)) -> f#(f(a(), h(f(a(), x))), y)) (f#(x, f(a(), y)) -> f#(f(a(), h(f(a(), x))), y), f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y)))} SCCS: Scc: {f#(x, f(a(), y)) -> f#(f(a(), h(f(a(), x))), y), f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y))} SCC: Strict: {f#(x, f(a(), y)) -> f#(f(a(), h(f(a(), x))), y), f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y))} Weak: {f(x, f(a(), y)) -> f(a(), f(f(a(), h(f(a(), x))), y))} POLY: Argument Filtering: pi(h) = [], pi(a) = [], pi(f#) = 1, pi(f) = [1] Usable Rules: {} Interpretation: [f](x0) = x0 + 1 Strict: {f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y))} Weak: {f(x, f(a(), y)) -> f(a(), f(f(a(), h(f(a(), x))), y))} EDG: {(f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y)), f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y)))} SCCS: Scc: {f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y))} SCC: Strict: {f#(x, f(a(), y)) -> f#(a(), f(f(a(), h(f(a(), x))), y))} Weak: {f(x, f(a(), y)) -> f(a(), f(f(a(), h(f(a(), x))), y))} Fail