/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: active(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(plus(X1,X2)) -> plus(X1,active(X2)) active(plus(X1,X2)) -> plus(active(X1),X2) active(s(X)) -> s(active(X)) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) proper(0()) -> ok(0()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(tt()) -> ok(tt()) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,and/2,plus/2,proper/1,s/1,top/1} / {0/0,mark/1,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {active,and,plus,proper,s,top} and constructors {0,mark,ok,tt} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: active(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(plus(X1,X2)) -> plus(X1,active(X2)) active(plus(X1,X2)) -> plus(active(X1),X2) active(s(X)) -> s(active(X)) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) proper(0()) -> ok(0()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(tt()) -> ok(tt()) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,and/2,plus/2,proper/1,s/1,top/1} / {0/0,mark/1,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {active,and,plus,proper,s,top} and constructors {0,mark,ok,tt} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:2: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: active(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(plus(X1,X2)) -> plus(X1,active(X2)) active(plus(X1,X2)) -> plus(active(X1),X2) active(s(X)) -> s(active(X)) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) proper(0()) -> ok(0()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(tt()) -> ok(tt()) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,and/2,plus/2,proper/1,s/1,top/1} / {0/0,mark/1,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {active,and,plus,proper,s,top} and constructors {0,mark,ok,tt} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: and(x,y){x -> mark(x)} = and(mark(x),y) ->^+ mark(and(x,y)) = C[and(x,y) = and(x,y){}] ** Step 1.b:1: Bounds. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: active(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(plus(X1,X2)) -> plus(X1,active(X2)) active(plus(X1,X2)) -> plus(active(X1),X2) active(s(X)) -> s(active(X)) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) proper(0()) -> ok(0()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(tt()) -> ok(tt()) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,and/2,plus/2,proper/1,s/1,top/1} / {0/0,mark/1,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {active,and,plus,proper,s,top} and constructors {0,mark,ok,tt} + 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_1() -> 13 active_0(1) -> 2 active_0(4) -> 2 active_0(5) -> 2 active_0(10) -> 2 active_1(1) -> 15 active_1(4) -> 15 active_1(5) -> 15 active_1(10) -> 15 active_2(13) -> 16 and_0(1,1) -> 3 and_0(1,4) -> 3 and_0(1,5) -> 3 and_0(1,10) -> 3 and_0(4,1) -> 3 and_0(4,4) -> 3 and_0(4,5) -> 3 and_0(4,10) -> 3 and_0(5,1) -> 3 and_0(5,4) -> 3 and_0(5,5) -> 3 and_0(5,10) -> 3 and_0(10,1) -> 3 and_0(10,4) -> 3 and_0(10,5) -> 3 and_0(10,10) -> 3 and_1(1,1) -> 11 and_1(1,4) -> 11 and_1(1,5) -> 11 and_1(1,10) -> 11 and_1(4,1) -> 11 and_1(4,4) -> 11 and_1(4,5) -> 11 and_1(4,10) -> 11 and_1(5,1) -> 11 and_1(5,4) -> 11 and_1(5,5) -> 11 and_1(5,10) -> 11 and_1(10,1) -> 11 and_1(10,4) -> 11 and_1(10,5) -> 11 and_1(10,10) -> 11 mark_0(1) -> 4 mark_0(4) -> 4 mark_0(5) -> 4 mark_0(10) -> 4 mark_1(11) -> 3 mark_1(11) -> 11 mark_1(12) -> 6 mark_1(12) -> 12 mark_1(14) -> 8 mark_1(14) -> 14 ok_0(1) -> 5 ok_0(4) -> 5 ok_0(5) -> 5 ok_0(10) -> 5 ok_1(11) -> 3 ok_1(11) -> 11 ok_1(12) -> 6 ok_1(12) -> 12 ok_1(13) -> 7 ok_1(13) -> 15 ok_1(14) -> 8 ok_1(14) -> 14 plus_0(1,1) -> 6 plus_0(1,4) -> 6 plus_0(1,5) -> 6 plus_0(1,10) -> 6 plus_0(4,1) -> 6 plus_0(4,4) -> 6 plus_0(4,5) -> 6 plus_0(4,10) -> 6 plus_0(5,1) -> 6 plus_0(5,4) -> 6 plus_0(5,5) -> 6 plus_0(5,10) -> 6 plus_0(10,1) -> 6 plus_0(10,4) -> 6 plus_0(10,5) -> 6 plus_0(10,10) -> 6 plus_1(1,1) -> 12 plus_1(1,4) -> 12 plus_1(1,5) -> 12 plus_1(1,10) -> 12 plus_1(4,1) -> 12 plus_1(4,4) -> 12 plus_1(4,5) -> 12 plus_1(4,10) -> 12 plus_1(5,1) -> 12 plus_1(5,4) -> 12 plus_1(5,5) -> 12 plus_1(5,10) -> 12 plus_1(10,1) -> 12 plus_1(10,4) -> 12 plus_1(10,5) -> 12 plus_1(10,10) -> 12 proper_0(1) -> 7 proper_0(4) -> 7 proper_0(5) -> 7 proper_0(10) -> 7 proper_1(1) -> 15 proper_1(4) -> 15 proper_1(5) -> 15 proper_1(10) -> 15 s_0(1) -> 8 s_0(4) -> 8 s_0(5) -> 8 s_0(10) -> 8 s_1(1) -> 14 s_1(4) -> 14 s_1(5) -> 14 s_1(10) -> 14 top_0(1) -> 9 top_0(4) -> 9 top_0(5) -> 9 top_0(10) -> 9 top_1(15) -> 9 top_2(16) -> 9 tt_0() -> 10 tt_1() -> 13 ** Step 1.b:2: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: active(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(plus(X1,X2)) -> plus(X1,active(X2)) active(plus(X1,X2)) -> plus(active(X1),X2) active(s(X)) -> s(active(X)) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) proper(0()) -> ok(0()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(tt()) -> ok(tt()) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,and/2,plus/2,proper/1,s/1,top/1} / {0/0,mark/1,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {active,and,plus,proper,s,top} and constructors {0,mark,ok,tt} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))