/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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: active(f(X)) -> f(active(X)) active(f(X)) -> mark(if(X,c(),f(true()))) active(if(X1,X2,X3)) -> if(X1,active(X2),X3) active(if(X1,X2,X3)) -> if(active(X1),X2,X3) active(if(false(),X,Y)) -> mark(Y) active(if(true(),X,Y)) -> mark(X) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) if(X1,mark(X2),X3) -> mark(if(X1,X2,X3)) if(mark(X1),X2,X3) -> mark(if(X1,X2,X3)) if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3)) proper(c()) -> ok(c()) proper(f(X)) -> f(proper(X)) proper(false()) -> ok(false()) proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3)) proper(true()) -> ok(true()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/1,if/3,proper/1,top/1} / {c/0,false/0,mark/1,ok/1,true/0} - Obligation: runtime complexity wrt. defined symbols {active,f,if,proper,top} and constructors {c,false,mark,ok,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: active(f(X)) -> f(active(X)) active(f(X)) -> mark(if(X,c(),f(true()))) active(if(X1,X2,X3)) -> if(X1,active(X2),X3) active(if(X1,X2,X3)) -> if(active(X1),X2,X3) active(if(false(),X,Y)) -> mark(Y) active(if(true(),X,Y)) -> mark(X) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) if(X1,mark(X2),X3) -> mark(if(X1,X2,X3)) if(mark(X1),X2,X3) -> mark(if(X1,X2,X3)) if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3)) proper(c()) -> ok(c()) proper(f(X)) -> f(proper(X)) proper(false()) -> ok(false()) proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3)) proper(true()) -> ok(true()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/1,if/3,proper/1,top/1} / {c/0,false/0,mark/1,ok/1,true/0} - Obligation: runtime complexity wrt. defined symbols {active,f,if,proper,top} and constructors {c,false,mark,ok,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:2: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: active(f(X)) -> f(active(X)) active(f(X)) -> mark(if(X,c(),f(true()))) active(if(X1,X2,X3)) -> if(X1,active(X2),X3) active(if(X1,X2,X3)) -> if(active(X1),X2,X3) active(if(false(),X,Y)) -> mark(Y) active(if(true(),X,Y)) -> mark(X) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) if(X1,mark(X2),X3) -> mark(if(X1,X2,X3)) if(mark(X1),X2,X3) -> mark(if(X1,X2,X3)) if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3)) proper(c()) -> ok(c()) proper(f(X)) -> f(proper(X)) proper(false()) -> ok(false()) proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3)) proper(true()) -> ok(true()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/1,if/3,proper/1,top/1} / {c/0,false/0,mark/1,ok/1,true/0} - Obligation: runtime complexity wrt. defined symbols {active,f,if,proper,top} and constructors {c,false,mark,ok,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(x){x -> mark(x)} = f(mark(x)) ->^+ mark(f(x)) = C[f(x) = f(x){}] ** Step 1.b:1: Bounds. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: active(f(X)) -> f(active(X)) active(f(X)) -> mark(if(X,c(),f(true()))) active(if(X1,X2,X3)) -> if(X1,active(X2),X3) active(if(X1,X2,X3)) -> if(active(X1),X2,X3) active(if(false(),X,Y)) -> mark(Y) active(if(true(),X,Y)) -> mark(X) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) if(X1,mark(X2),X3) -> mark(if(X1,X2,X3)) if(mark(X1),X2,X3) -> mark(if(X1,X2,X3)) if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3)) proper(c()) -> ok(c()) proper(f(X)) -> f(proper(X)) proper(false()) -> ok(false()) proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3)) proper(true()) -> ok(true()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/1,if/3,proper/1,top/1} / {c/0,false/0,mark/1,ok/1,true/0} - Obligation: runtime complexity wrt. defined symbols {active,f,if,proper,top} and constructors {c,false,mark,ok,true} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. active_0(2) -> 1 active_0(4) -> 1 active_0(6) -> 1 active_0(7) -> 1 active_0(10) -> 1 active_1(2) -> 14 active_1(4) -> 14 active_1(6) -> 14 active_1(7) -> 14 active_1(10) -> 14 active_2(13) -> 15 c_0() -> 2 c_1() -> 13 f_0(2) -> 3 f_0(4) -> 3 f_0(6) -> 3 f_0(7) -> 3 f_0(10) -> 3 f_1(2) -> 11 f_1(4) -> 11 f_1(6) -> 11 f_1(7) -> 11 f_1(10) -> 11 false_0() -> 4 false_1() -> 13 if_0(2,2,2) -> 5 if_0(2,2,4) -> 5 if_0(2,2,6) -> 5 if_0(2,2,7) -> 5 if_0(2,2,10) -> 5 if_0(2,4,2) -> 5 if_0(2,4,4) -> 5 if_0(2,4,6) -> 5 if_0(2,4,7) -> 5 if_0(2,4,10) -> 5 if_0(2,6,2) -> 5 if_0(2,6,4) -> 5 if_0(2,6,6) -> 5 if_0(2,6,7) -> 5 if_0(2,6,10) -> 5 if_0(2,7,2) -> 5 if_0(2,7,4) -> 5 if_0(2,7,6) -> 5 if_0(2,7,7) -> 5 if_0(2,7,10) -> 5 if_0(2,10,2) -> 5 if_0(2,10,4) -> 5 if_0(2,10,6) -> 5 if_0(2,10,7) -> 5 if_0(2,10,10) -> 5 if_0(4,2,2) -> 5 if_0(4,2,4) -> 5 if_0(4,2,6) -> 5 if_0(4,2,7) -> 5 if_0(4,2,10) -> 5 if_0(4,4,2) -> 5 if_0(4,4,4) -> 5 if_0(4,4,6) -> 5 if_0(4,4,7) -> 5 if_0(4,4,10) -> 5 if_0(4,6,2) -> 5 if_0(4,6,4) -> 5 if_0(4,6,6) -> 5 if_0(4,6,7) -> 5 if_0(4,6,10) -> 5 if_0(4,7,2) -> 5 if_0(4,7,4) -> 5 if_0(4,7,6) -> 5 if_0(4,7,7) -> 5 if_0(4,7,10) -> 5 if_0(4,10,2) -> 5 if_0(4,10,4) -> 5 if_0(4,10,6) -> 5 if_0(4,10,7) -> 5 if_0(4,10,10) -> 5 if_0(6,2,2) -> 5 if_0(6,2,4) -> 5 if_0(6,2,6) -> 5 if_0(6,2,7) -> 5 if_0(6,2,10) -> 5 if_0(6,4,2) -> 5 if_0(6,4,4) -> 5 if_0(6,4,6) -> 5 if_0(6,4,7) -> 5 if_0(6,4,10) -> 5 if_0(6,6,2) -> 5 if_0(6,6,4) -> 5 if_0(6,6,6) -> 5 if_0(6,6,7) -> 5 if_0(6,6,10) -> 5 if_0(6,7,2) -> 5 if_0(6,7,4) -> 5 if_0(6,7,6) -> 5 if_0(6,7,7) -> 5 if_0(6,7,10) -> 5 if_0(6,10,2) -> 5 if_0(6,10,4) -> 5 if_0(6,10,6) -> 5 if_0(6,10,7) -> 5 if_0(6,10,10) -> 5 if_0(7,2,2) -> 5 if_0(7,2,4) -> 5 if_0(7,2,6) -> 5 if_0(7,2,7) -> 5 if_0(7,2,10) -> 5 if_0(7,4,2) -> 5 if_0(7,4,4) -> 5 if_0(7,4,6) -> 5 if_0(7,4,7) -> 5 if_0(7,4,10) -> 5 if_0(7,6,2) -> 5 if_0(7,6,4) -> 5 if_0(7,6,6) -> 5 if_0(7,6,7) -> 5 if_0(7,6,10) -> 5 if_0(7,7,2) -> 5 if_0(7,7,4) -> 5 if_0(7,7,6) -> 5 if_0(7,7,7) -> 5 if_0(7,7,10) -> 5 if_0(7,10,2) -> 5 if_0(7,10,4) -> 5 if_0(7,10,6) -> 5 if_0(7,10,7) -> 5 if_0(7,10,10) -> 5 if_0(10,2,2) -> 5 if_0(10,2,4) -> 5 if_0(10,2,6) -> 5 if_0(10,2,7) -> 5 if_0(10,2,10) -> 5 if_0(10,4,2) -> 5 if_0(10,4,4) -> 5 if_0(10,4,6) -> 5 if_0(10,4,7) -> 5 if_0(10,4,10) -> 5 if_0(10,6,2) -> 5 if_0(10,6,4) -> 5 if_0(10,6,6) -> 5 if_0(10,6,7) -> 5 if_0(10,6,10) -> 5 if_0(10,7,2) -> 5 if_0(10,7,4) -> 5 if_0(10,7,6) -> 5 if_0(10,7,7) -> 5 if_0(10,7,10) -> 5 if_0(10,10,2) -> 5 if_0(10,10,4) -> 5 if_0(10,10,6) -> 5 if_0(10,10,7) -> 5 if_0(10,10,10) -> 5 if_1(2,2,2) -> 12 if_1(2,2,4) -> 12 if_1(2,2,6) -> 12 if_1(2,2,7) -> 12 if_1(2,2,10) -> 12 if_1(2,4,2) -> 12 if_1(2,4,4) -> 12 if_1(2,4,6) -> 12 if_1(2,4,7) -> 12 if_1(2,4,10) -> 12 if_1(2,6,2) -> 12 if_1(2,6,4) -> 12 if_1(2,6,6) -> 12 if_1(2,6,7) -> 12 if_1(2,6,10) -> 12 if_1(2,7,2) -> 12 if_1(2,7,4) -> 12 if_1(2,7,6) -> 12 if_1(2,7,7) -> 12 if_1(2,7,10) -> 12 if_1(2,10,2) -> 12 if_1(2,10,4) -> 12 if_1(2,10,6) -> 12 if_1(2,10,7) -> 12 if_1(2,10,10) -> 12 if_1(4,2,2) -> 12 if_1(4,2,4) -> 12 if_1(4,2,6) -> 12 if_1(4,2,7) -> 12 if_1(4,2,10) -> 12 if_1(4,4,2) -> 12 if_1(4,4,4) -> 12 if_1(4,4,6) -> 12 if_1(4,4,7) -> 12 if_1(4,4,10) -> 12 if_1(4,6,2) -> 12 if_1(4,6,4) -> 12 if_1(4,6,6) -> 12 if_1(4,6,7) -> 12 if_1(4,6,10) -> 12 if_1(4,7,2) -> 12 if_1(4,7,4) -> 12 if_1(4,7,6) -> 12 if_1(4,7,7) -> 12 if_1(4,7,10) -> 12 if_1(4,10,2) -> 12 if_1(4,10,4) -> 12 if_1(4,10,6) -> 12 if_1(4,10,7) -> 12 if_1(4,10,10) -> 12 if_1(6,2,2) -> 12 if_1(6,2,4) -> 12 if_1(6,2,6) -> 12 if_1(6,2,7) -> 12 if_1(6,2,10) -> 12 if_1(6,4,2) -> 12 if_1(6,4,4) -> 12 if_1(6,4,6) -> 12 if_1(6,4,7) -> 12 if_1(6,4,10) -> 12 if_1(6,6,2) -> 12 if_1(6,6,4) -> 12 if_1(6,6,6) -> 12 if_1(6,6,7) -> 12 if_1(6,6,10) -> 12 if_1(6,7,2) -> 12 if_1(6,7,4) -> 12 if_1(6,7,6) -> 12 if_1(6,7,7) -> 12 if_1(6,7,10) -> 12 if_1(6,10,2) -> 12 if_1(6,10,4) -> 12 if_1(6,10,6) -> 12 if_1(6,10,7) -> 12 if_1(6,10,10) -> 12 if_1(7,2,2) -> 12 if_1(7,2,4) -> 12 if_1(7,2,6) -> 12 if_1(7,2,7) -> 12 if_1(7,2,10) -> 12 if_1(7,4,2) -> 12 if_1(7,4,4) -> 12 if_1(7,4,6) -> 12 if_1(7,4,7) -> 12 if_1(7,4,10) -> 12 if_1(7,6,2) -> 12 if_1(7,6,4) -> 12 if_1(7,6,6) -> 12 if_1(7,6,7) -> 12 if_1(7,6,10) -> 12 if_1(7,7,2) -> 12 if_1(7,7,4) -> 12 if_1(7,7,6) -> 12 if_1(7,7,7) -> 12 if_1(7,7,10) -> 12 if_1(7,10,2) -> 12 if_1(7,10,4) -> 12 if_1(7,10,6) -> 12 if_1(7,10,7) -> 12 if_1(7,10,10) -> 12 if_1(10,2,2) -> 12 if_1(10,2,4) -> 12 if_1(10,2,6) -> 12 if_1(10,2,7) -> 12 if_1(10,2,10) -> 12 if_1(10,4,2) -> 12 if_1(10,4,4) -> 12 if_1(10,4,6) -> 12 if_1(10,4,7) -> 12 if_1(10,4,10) -> 12 if_1(10,6,2) -> 12 if_1(10,6,4) -> 12 if_1(10,6,6) -> 12 if_1(10,6,7) -> 12 if_1(10,6,10) -> 12 if_1(10,7,2) -> 12 if_1(10,7,4) -> 12 if_1(10,7,6) -> 12 if_1(10,7,7) -> 12 if_1(10,7,10) -> 12 if_1(10,10,2) -> 12 if_1(10,10,4) -> 12 if_1(10,10,6) -> 12 if_1(10,10,7) -> 12 if_1(10,10,10) -> 12 mark_0(2) -> 6 mark_0(4) -> 6 mark_0(6) -> 6 mark_0(7) -> 6 mark_0(10) -> 6 mark_1(11) -> 3 mark_1(11) -> 11 mark_1(12) -> 5 mark_1(12) -> 12 ok_0(2) -> 7 ok_0(4) -> 7 ok_0(6) -> 7 ok_0(7) -> 7 ok_0(10) -> 7 ok_1(11) -> 3 ok_1(11) -> 11 ok_1(12) -> 5 ok_1(12) -> 12 ok_1(13) -> 8 ok_1(13) -> 14 proper_0(2) -> 8 proper_0(4) -> 8 proper_0(6) -> 8 proper_0(7) -> 8 proper_0(10) -> 8 proper_1(2) -> 14 proper_1(4) -> 14 proper_1(6) -> 14 proper_1(7) -> 14 proper_1(10) -> 14 top_0(2) -> 9 top_0(4) -> 9 top_0(6) -> 9 top_0(7) -> 9 top_0(10) -> 9 top_1(14) -> 9 top_2(15) -> 9 true_0() -> 10 true_1() -> 13 ** Step 1.b:2: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: active(f(X)) -> f(active(X)) active(f(X)) -> mark(if(X,c(),f(true()))) active(if(X1,X2,X3)) -> if(X1,active(X2),X3) active(if(X1,X2,X3)) -> if(active(X1),X2,X3) active(if(false(),X,Y)) -> mark(Y) active(if(true(),X,Y)) -> mark(X) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) if(X1,mark(X2),X3) -> mark(if(X1,X2,X3)) if(mark(X1),X2,X3) -> mark(if(X1,X2,X3)) if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3)) proper(c()) -> ok(c()) proper(f(X)) -> f(proper(X)) proper(false()) -> ok(false()) proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3)) proper(true()) -> ok(true()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/1,if/3,proper/1,top/1} / {c/0,false/0,mark/1,ok/1,true/0} - Obligation: runtime complexity wrt. defined symbols {active,f,if,proper,top} and constructors {c,false,mark,ok,true} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))