*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: a__c(X) -> c(X) a__c(X) -> d(X) a__f(X) -> f(X) a__f(f(X)) -> a__c(f(g(f(X)))) a__h(X) -> a__c(d(X)) a__h(X) -> h(X) mark(c(X)) -> a__c(X) mark(d(X)) -> d(X) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> g(X) mark(h(X)) -> a__h(mark(X)) Weak DP Rules: Weak TRS Rules: Signature: {a__c/1,a__f/1,a__h/1,mark/1} / {c/1,d/1,f/1,g/1,h/1} Obligation: Innermost basic terms: {a__c,a__f,a__h,mark}/{c,d,f,g,h} Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} Proof: The problem is match-bounded by 3. The enriched problem is compatible with follwoing automaton. a__c_0(2) -> 1 a__c_1(1) -> 1 a__c_1(2) -> 1 a__c_1(2) -> 5 a__c_1(3) -> 1 a__c_2(6) -> 1 a__c_2(6) -> 5 a__f_0(2) -> 1 a__f_1(5) -> 1 a__f_1(5) -> 5 a__h_0(2) -> 1 a__h_1(5) -> 1 a__h_1(5) -> 5 c_0(2) -> 2 c_1(2) -> 1 c_2(1) -> 1 c_2(2) -> 1 c_2(2) -> 5 c_2(3) -> 1 c_3(6) -> 1 c_3(6) -> 5 d_0(2) -> 2 d_1(2) -> 1 d_1(2) -> 5 d_2(1) -> 1 d_2(2) -> 1 d_2(2) -> 5 d_2(3) -> 1 d_2(5) -> 6 d_3(6) -> 1 d_3(6) -> 5 f_0(2) -> 2 f_1(2) -> 1 f_1(4) -> 3 f_2(5) -> 1 f_2(5) -> 5 f_2(7) -> 6 g_0(2) -> 2 g_1(1) -> 4 g_1(2) -> 1 g_1(2) -> 5 g_2(5) -> 7 h_0(2) -> 2 h_1(2) -> 1 h_2(5) -> 1 h_2(5) -> 5 mark_0(2) -> 1 mark_1(2) -> 5 *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: a__c(X) -> c(X) a__c(X) -> d(X) a__f(X) -> f(X) a__f(f(X)) -> a__c(f(g(f(X)))) a__h(X) -> a__c(d(X)) a__h(X) -> h(X) mark(c(X)) -> a__c(X) mark(d(X)) -> d(X) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> g(X) mark(h(X)) -> a__h(mark(X)) Signature: {a__c/1,a__f/1,a__h/1,mark/1} / {c/1,d/1,f/1,g/1,h/1} Obligation: Innermost basic terms: {a__c,a__f,a__h,mark}/{c,d,f,g,h} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).