*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: f(x,h1(y,z)) -> h2(0(),x,h1(y,z)) f(j(x,y),y) -> g(f(x,k(y))) g(h2(x,y,h1(z,u))) -> h2(s(x),y,h1(z,u)) h2(x,j(y,h1(z,u)),h1(z,u)) -> h2(s(x),y,h1(s(z),u)) i(f(x,h(y))) -> y i(h2(s(x),y,h1(x,z))) -> z k(h(x)) -> h1(0(),x) k(h1(x,y)) -> h1(s(x),y) Weak DP Rules: Weak TRS Rules: Signature: {f/2,g/1,h2/3,i/1,k/1} / {0/0,h/1,h1/2,j/2,s/1} Obligation: Innermost basic terms: {f,g,h2,i,k}/{0,h,h1,j,s} Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} Proof: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. 0_0() -> 2 0_1() -> 3 0_2() -> 7 f_0(2,2) -> 1 f_1(2,6) -> 5 g_0(2) -> 1 g_1(5) -> 1 g_1(5) -> 5 h_0(2) -> 2 h1_0(2,2) -> 2 h1_1(2,2) -> 4 h1_1(3,2) -> 1 h1_1(3,2) -> 6 h1_2(3,2) -> 8 h2_0(2,2,2) -> 1 h2_1(3,2,4) -> 1 h2_1(3,2,6) -> 5 h2_1(10,2,6) -> 5 h2_2(7,2,8) -> 5 h2_2(9,2,8) -> 1 h2_2(9,2,8) -> 5 i_0(2) -> 1 j_0(2,2) -> 2 k_0(2) -> 1 k_1(2) -> 6 s_0(2) -> 2 s_1(2) -> 2 s_1(2) -> 3 s_1(3) -> 3 s_1(7) -> 10 s_1(9) -> 3 s_1(10) -> 3 s_2(3) -> 9 s_2(7) -> 9 s_2(9) -> 9 s_2(10) -> 9 *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: f(x,h1(y,z)) -> h2(0(),x,h1(y,z)) f(j(x,y),y) -> g(f(x,k(y))) g(h2(x,y,h1(z,u))) -> h2(s(x),y,h1(z,u)) h2(x,j(y,h1(z,u)),h1(z,u)) -> h2(s(x),y,h1(s(z),u)) i(f(x,h(y))) -> y i(h2(s(x),y,h1(x,z))) -> z k(h(x)) -> h1(0(),x) k(h1(x,y)) -> h1(s(x),y) Signature: {f/2,g/1,h2/3,i/1,k/1} / {0/0,h/1,h1/2,j/2,s/1} Obligation: Innermost basic terms: {f,g,h2,i,k}/{0,h,h1,j,s} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).