/bin/sh: line 1: 42295 Quit (core dumped) z3 -T:13.845 -smt2 /tmp/SMTP42123-86 > /tmp/SMTS42123-87 /bin/sh: line 1: 42296 Quit (core dumped) z3 -T:13.845 -smt2 /tmp/SMTP42123-72 > /tmp/SMTS42123-73 /bin/sh: line 1: 42290 Quit (core dumped) z3 -T:13.845 -smt2 /tmp/SMTP42123-64 > /tmp/SMTS42123-65 /bin/sh: line 1: 42298 Quit (core dumped) z3 -T:13.845 -smt2 /tmp/SMTP42123-78 > /tmp/SMTS42123-79 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: innermost 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: innermost 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: innermost 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: 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 = minimal, enrichment = match} + Details: 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 ** Step 1.b:2: 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))