*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: f(f(x)) -> f(c(f(x))) f(f(x)) -> f(d(f(x))) g(c(x)) -> x g(c(1())) -> g(d(h(0()))) g(c(h(0()))) -> g(d(1())) g(d(x)) -> x g(h(x)) -> g(x) Weak DP Rules: Weak TRS Rules: Signature: {f/1,g/1} / {0/0,1/0,c/1,d/1,h/1} Obligation: Full basic terms: {f,g}/{0,1,c,d,h} Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} Proof: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. 0_0() -> 1 0_0() -> 2 0_1() -> 5 1_0() -> 1 1_0() -> 2 1_1() -> 1 1_1() -> 4 c_0(2) -> 1 c_0(2) -> 2 d_0(2) -> 1 d_0(2) -> 2 d_1(4) -> 3 f_0(2) -> 1 g_0(2) -> 1 g_1(2) -> 1 g_1(3) -> 1 h_0(2) -> 1 h_0(2) -> 2 h_1(5) -> 1 h_1(5) -> 4 2 -> 1 4 -> 1 *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: f(f(x)) -> f(c(f(x))) f(f(x)) -> f(d(f(x))) g(c(x)) -> x g(c(1())) -> g(d(h(0()))) g(c(h(0()))) -> g(d(1())) g(d(x)) -> x g(h(x)) -> g(x) Signature: {f/1,g/1} / {0/0,1/0,c/1,d/1,h/1} Obligation: Full basic terms: {f,g}/{0,1,c,d,h} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).