*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: f(x,g(y,z)) -> g(f(x,y),z) f(x,nil()) -> g(nil(),x) norm(g(x,y)) -> s(norm(x)) norm(nil()) -> 0() rem(g(x,y),0()) -> g(x,y) rem(g(x,y),s(z)) -> rem(x,z) rem(nil(),y) -> nil() Weak DP Rules: Weak TRS Rules: Signature: {f/2,norm/1,rem/2} / {0/0,g/2,nil/0,s/1} Obligation: Innermost basic terms: {f,norm,rem}/{0,g,nil,s} 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() -> 2 0_1() -> 1 0_1() -> 4 f_0(2,2) -> 1 f_1(2,2) -> 3 g_0(2,2) -> 2 g_1(2,2) -> 1 g_1(3,2) -> 1 g_1(3,2) -> 3 nil_0() -> 2 nil_1() -> 1 nil_1() -> 3 norm_0(2) -> 1 norm_1(2) -> 4 rem_0(2,2) -> 1 rem_1(2,2) -> 1 s_0(2) -> 2 s_1(4) -> 1 s_1(4) -> 4 *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: f(x,g(y,z)) -> g(f(x,y),z) f(x,nil()) -> g(nil(),x) norm(g(x,y)) -> s(norm(x)) norm(nil()) -> 0() rem(g(x,y),0()) -> g(x,y) rem(g(x,y),s(z)) -> rem(x,z) rem(nil(),y) -> nil() Signature: {f/2,norm/1,rem/2} / {0/0,g/2,nil/0,s/1} Obligation: Innermost basic terms: {f,norm,rem}/{0,g,nil,s} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).