/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^1)) * Step 1: Sum. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__f(X)) -> f(X) f(X) -> n__f(X) f(0()) -> cons(0(),n__f(s(0()))) f(s(0())) -> f(p(s(0()))) p(s(X)) -> X - Signature: {activate/1,f/1,p/1} / {0/0,cons/2,n__f/1,s/1} - Obligation: runtime complexity wrt. defined symbols {activate,f,p} and constructors {0,cons,n__f,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: ToInnermost. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__f(X)) -> f(X) f(X) -> n__f(X) f(0()) -> cons(0(),n__f(s(0()))) f(s(0())) -> f(p(s(0()))) p(s(X)) -> X - Signature: {activate/1,f/1,p/1} / {0/0,cons/2,n__f/1,s/1} - Obligation: runtime complexity wrt. defined symbols {activate,f,p} and constructors {0,cons,n__f,s} + Applied Processor: ToInnermost + Details: switch to innermost, as the system is overlay and right linear and does not contain weak rules * Step 3: Bounds. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__f(X)) -> f(X) f(X) -> n__f(X) f(0()) -> cons(0(),n__f(s(0()))) f(s(0())) -> f(p(s(0()))) p(s(X)) -> X - Signature: {activate/1,f/1,p/1} / {0/0,cons/2,n__f/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,f,p} and constructors {0,cons,n__f,s} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. 0_0() -> 1 0_0() -> 2 0_0() -> 6 0_1() -> 1 0_1() -> 2 0_1() -> 6 0_1() -> 8 0_1() -> 11 0_2() -> 12 0_2() -> 15 activate_0(1) -> 2 activate_0(3) -> 2 activate_0(5) -> 2 activate_0(7) -> 2 cons_0(1,1) -> 2 cons_0(1,1) -> 3 cons_0(1,1) -> 6 cons_0(1,3) -> 2 cons_0(1,3) -> 3 cons_0(1,3) -> 6 cons_0(1,5) -> 2 cons_0(1,5) -> 3 cons_0(1,5) -> 6 cons_0(1,7) -> 2 cons_0(1,7) -> 3 cons_0(1,7) -> 6 cons_0(3,1) -> 2 cons_0(3,1) -> 3 cons_0(3,1) -> 6 cons_0(3,3) -> 2 cons_0(3,3) -> 3 cons_0(3,3) -> 6 cons_0(3,5) -> 2 cons_0(3,5) -> 3 cons_0(3,5) -> 6 cons_0(3,7) -> 2 cons_0(3,7) -> 3 cons_0(3,7) -> 6 cons_0(5,1) -> 2 cons_0(5,1) -> 3 cons_0(5,1) -> 6 cons_0(5,3) -> 2 cons_0(5,3) -> 3 cons_0(5,3) -> 6 cons_0(5,5) -> 2 cons_0(5,5) -> 3 cons_0(5,5) -> 6 cons_0(5,7) -> 2 cons_0(5,7) -> 3 cons_0(5,7) -> 6 cons_0(7,1) -> 2 cons_0(7,1) -> 3 cons_0(7,1) -> 6 cons_0(7,3) -> 2 cons_0(7,3) -> 3 cons_0(7,3) -> 6 cons_0(7,5) -> 2 cons_0(7,5) -> 3 cons_0(7,5) -> 6 cons_0(7,7) -> 2 cons_0(7,7) -> 3 cons_0(7,7) -> 6 cons_1(8,9) -> 2 cons_1(11,9) -> 4 cons_2(12,13) -> 2 cons_2(15,13) -> 4 f_0(1) -> 4 f_0(3) -> 4 f_0(5) -> 4 f_0(7) -> 4 f_1(1) -> 2 f_1(1) -> 4 f_1(3) -> 2 f_1(5) -> 2 f_1(7) -> 2 n__f_0(1) -> 2 n__f_0(1) -> 5 n__f_0(1) -> 6 n__f_0(3) -> 2 n__f_0(3) -> 5 n__f_0(3) -> 6 n__f_0(5) -> 2 n__f_0(5) -> 5 n__f_0(5) -> 6 n__f_0(7) -> 2 n__f_0(7) -> 5 n__f_0(7) -> 6 n__f_1(1) -> 4 n__f_1(3) -> 4 n__f_1(5) -> 4 n__f_1(7) -> 4 n__f_1(10) -> 9 n__f_2(1) -> 2 n__f_2(1) -> 4 n__f_2(3) -> 2 n__f_2(5) -> 2 n__f_2(7) -> 2 n__f_2(14) -> 13 p_0(1) -> 6 p_0(3) -> 6 p_0(5) -> 6 p_0(7) -> 6 p_1(10) -> 1 p_1(10) -> 2 p_1(10) -> 6 s_0(1) -> 2 s_0(1) -> 6 s_0(1) -> 7 s_0(3) -> 2 s_0(3) -> 6 s_0(3) -> 7 s_0(5) -> 2 s_0(5) -> 6 s_0(5) -> 7 s_0(7) -> 2 s_0(7) -> 6 s_0(7) -> 7 s_1(11) -> 10 s_2(15) -> 14 1 -> 2 1 -> 6 3 -> 2 3 -> 6 5 -> 2 5 -> 6 7 -> 2 7 -> 6 11 -> 1 11 -> 2 11 -> 6 * Step 4: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: activate(X) -> X activate(n__f(X)) -> f(X) f(X) -> n__f(X) f(0()) -> cons(0(),n__f(s(0()))) f(s(0())) -> f(p(s(0()))) p(s(X)) -> X - Signature: {activate/1,f/1,p/1} / {0/0,cons/2,n__f/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,f,p} and constructors {0,cons,n__f,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))