/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1),O(n^1)) * Step 1: Sum. WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: 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: runtime complexity wrt. defined symbols {a__c,a__f,a__h,mark} and constructors {c,d,f,g,h} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: 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: runtime complexity wrt. defined symbols {a__c,a__f,a__h,mark} and constructors {c,d,f,g,h} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:2: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: 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: runtime complexity wrt. defined symbols {a__c,a__f,a__h,mark} and constructors {c,d,f,g,h} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: mark(x){x -> f(x)} = mark(f(x)) ->^+ a__f(mark(x)) = C[mark(x) = mark(x){}] ** Step 1.b:1: ToInnermost. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: 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: runtime complexity wrt. defined symbols {a__c,a__f,a__h,mark} and constructors {c,d,f,g,h} + Applied Processor: ToInnermost + Details: switch to innermost, as the system is overlay and right linear and does not contain weak rules ** Step 1.b:2: Bounds. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: 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 runtime complexity wrt. defined symbols {a__c,a__f,a__h,mark} and constructors {c,d,f,g,h} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 3. The enriched problem is compatible with follwoing automaton. a__c_0(4) -> 1 a__c_0(5) -> 1 a__c_0(6) -> 1 a__c_0(7) -> 1 a__c_0(8) -> 1 a__c_1(1) -> 3 a__c_1(4) -> 9 a__c_1(4) -> 12 a__c_1(5) -> 9 a__c_1(5) -> 12 a__c_1(6) -> 9 a__c_1(6) -> 12 a__c_1(7) -> 9 a__c_1(7) -> 12 a__c_1(8) -> 9 a__c_1(8) -> 12 a__c_1(10) -> 2 a__c_2(13) -> 9 a__c_2(13) -> 12 a__f_0(4) -> 2 a__f_0(5) -> 2 a__f_0(6) -> 2 a__f_0(7) -> 2 a__f_0(8) -> 2 a__f_1(12) -> 9 a__f_1(12) -> 12 a__h_0(4) -> 3 a__h_0(5) -> 3 a__h_0(6) -> 3 a__h_0(7) -> 3 a__h_0(8) -> 3 a__h_1(12) -> 9 a__h_1(12) -> 12 c_0(4) -> 4 c_0(5) -> 4 c_0(6) -> 4 c_0(7) -> 4 c_0(8) -> 4 c_1(4) -> 1 c_1(5) -> 1 c_1(6) -> 1 c_1(7) -> 1 c_1(8) -> 1 c_2(1) -> 3 c_2(4) -> 9 c_2(4) -> 12 c_2(5) -> 9 c_2(5) -> 12 c_2(6) -> 9 c_2(6) -> 12 c_2(7) -> 9 c_2(7) -> 12 c_2(8) -> 9 c_2(8) -> 12 c_2(10) -> 2 c_3(13) -> 9 c_3(13) -> 12 d_0(4) -> 5 d_0(5) -> 5 d_0(6) -> 5 d_0(7) -> 5 d_0(8) -> 5 d_1(4) -> 1 d_1(4) -> 9 d_1(4) -> 12 d_1(5) -> 1 d_1(5) -> 9 d_1(5) -> 12 d_1(6) -> 1 d_1(6) -> 9 d_1(6) -> 12 d_1(7) -> 1 d_1(7) -> 9 d_1(7) -> 12 d_1(8) -> 1 d_1(8) -> 9 d_1(8) -> 12 d_2(1) -> 3 d_2(4) -> 9 d_2(4) -> 12 d_2(5) -> 9 d_2(5) -> 12 d_2(6) -> 9 d_2(6) -> 12 d_2(7) -> 9 d_2(7) -> 12 d_2(8) -> 9 d_2(8) -> 12 d_2(10) -> 2 d_2(12) -> 13 d_3(13) -> 9 d_3(13) -> 12 f_0(4) -> 6 f_0(5) -> 6 f_0(6) -> 6 f_0(7) -> 6 f_0(8) -> 6 f_1(4) -> 2 f_1(5) -> 2 f_1(6) -> 2 f_1(7) -> 2 f_1(8) -> 2 f_1(11) -> 10 f_2(12) -> 9 f_2(12) -> 12 f_2(14) -> 13 g_0(4) -> 7 g_0(5) -> 7 g_0(6) -> 7 g_0(7) -> 7 g_0(8) -> 7 g_1(2) -> 11 g_1(4) -> 9 g_1(4) -> 12 g_1(5) -> 9 g_1(5) -> 12 g_1(6) -> 9 g_1(6) -> 12 g_1(7) -> 9 g_1(7) -> 12 g_1(8) -> 9 g_1(8) -> 12 g_2(12) -> 14 h_0(4) -> 8 h_0(5) -> 8 h_0(6) -> 8 h_0(7) -> 8 h_0(8) -> 8 h_1(4) -> 3 h_1(5) -> 3 h_1(6) -> 3 h_1(7) -> 3 h_1(8) -> 3 h_2(12) -> 9 h_2(12) -> 12 mark_0(4) -> 9 mark_0(5) -> 9 mark_0(6) -> 9 mark_0(7) -> 9 mark_0(8) -> 9 mark_1(4) -> 12 mark_1(5) -> 12 mark_1(6) -> 12 mark_1(7) -> 12 mark_1(8) -> 12 ** Step 1.b:3: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: 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 runtime complexity wrt. defined symbols {a__c,a__f,a__h,mark} and constructors {c,d,f,g,h} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))