/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: U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(plus(X1,X2)) -> plus(X1,active(X2)) active(plus(X1,X2)) -> plus(active(X1),X2) active(s(X)) -> s(active(X)) 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(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) 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: {U11/3,U12/3,active/1,plus/2,proper/1,s/1,top/1} / {0/0,mark/1,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {U11,U12,active,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: U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(plus(X1,X2)) -> plus(X1,active(X2)) active(plus(X1,X2)) -> plus(active(X1),X2) active(s(X)) -> s(active(X)) 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(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) 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: {U11/3,U12/3,active/1,plus/2,proper/1,s/1,top/1} / {0/0,mark/1,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {U11,U12,active,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: U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(plus(X1,X2)) -> plus(X1,active(X2)) active(plus(X1,X2)) -> plus(active(X1),X2) active(s(X)) -> s(active(X)) 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(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) 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: {U11/3,U12/3,active/1,plus/2,proper/1,s/1,top/1} / {0/0,mark/1,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {U11,U12,active,plus,proper,s,top} and constructors {0,mark,ok,tt} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: U11(x,y,z){x -> mark(x)} = U11(mark(x),y,z) ->^+ mark(U11(x,y,z)) = C[U11(x,y,z) = U11(x,y,z){}] ** Step 1.b:1: Bounds. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(plus(X1,X2)) -> plus(X1,active(X2)) active(plus(X1,X2)) -> plus(active(X1),X2) active(s(X)) -> s(active(X)) 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(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) 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: {U11/3,U12/3,active/1,plus/2,proper/1,s/1,top/1} / {0/0,mark/1,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {U11,U12,active,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() -> 15 U11_0(1,1,1) -> 2 U11_0(1,1,5) -> 2 U11_0(1,1,6) -> 2 U11_0(1,1,11) -> 2 U11_0(1,5,1) -> 2 U11_0(1,5,5) -> 2 U11_0(1,5,6) -> 2 U11_0(1,5,11) -> 2 U11_0(1,6,1) -> 2 U11_0(1,6,5) -> 2 U11_0(1,6,6) -> 2 U11_0(1,6,11) -> 2 U11_0(1,11,1) -> 2 U11_0(1,11,5) -> 2 U11_0(1,11,6) -> 2 U11_0(1,11,11) -> 2 U11_0(5,1,1) -> 2 U11_0(5,1,5) -> 2 U11_0(5,1,6) -> 2 U11_0(5,1,11) -> 2 U11_0(5,5,1) -> 2 U11_0(5,5,5) -> 2 U11_0(5,5,6) -> 2 U11_0(5,5,11) -> 2 U11_0(5,6,1) -> 2 U11_0(5,6,5) -> 2 U11_0(5,6,6) -> 2 U11_0(5,6,11) -> 2 U11_0(5,11,1) -> 2 U11_0(5,11,5) -> 2 U11_0(5,11,6) -> 2 U11_0(5,11,11) -> 2 U11_0(6,1,1) -> 2 U11_0(6,1,5) -> 2 U11_0(6,1,6) -> 2 U11_0(6,1,11) -> 2 U11_0(6,5,1) -> 2 U11_0(6,5,5) -> 2 U11_0(6,5,6) -> 2 U11_0(6,5,11) -> 2 U11_0(6,6,1) -> 2 U11_0(6,6,5) -> 2 U11_0(6,6,6) -> 2 U11_0(6,6,11) -> 2 U11_0(6,11,1) -> 2 U11_0(6,11,5) -> 2 U11_0(6,11,6) -> 2 U11_0(6,11,11) -> 2 U11_0(11,1,1) -> 2 U11_0(11,1,5) -> 2 U11_0(11,1,6) -> 2 U11_0(11,1,11) -> 2 U11_0(11,5,1) -> 2 U11_0(11,5,5) -> 2 U11_0(11,5,6) -> 2 U11_0(11,5,11) -> 2 U11_0(11,6,1) -> 2 U11_0(11,6,5) -> 2 U11_0(11,6,6) -> 2 U11_0(11,6,11) -> 2 U11_0(11,11,1) -> 2 U11_0(11,11,5) -> 2 U11_0(11,11,6) -> 2 U11_0(11,11,11) -> 2 U11_1(1,1,1) -> 12 U11_1(1,1,5) -> 12 U11_1(1,1,6) -> 12 U11_1(1,1,11) -> 12 U11_1(1,5,1) -> 12 U11_1(1,5,5) -> 12 U11_1(1,5,6) -> 12 U11_1(1,5,11) -> 12 U11_1(1,6,1) -> 12 U11_1(1,6,5) -> 12 U11_1(1,6,6) -> 12 U11_1(1,6,11) -> 12 U11_1(1,11,1) -> 12 U11_1(1,11,5) -> 12 U11_1(1,11,6) -> 12 U11_1(1,11,11) -> 12 U11_1(5,1,1) -> 12 U11_1(5,1,5) -> 12 U11_1(5,1,6) -> 12 U11_1(5,1,11) -> 12 U11_1(5,5,1) -> 12 U11_1(5,5,5) -> 12 U11_1(5,5,6) -> 12 U11_1(5,5,11) -> 12 U11_1(5,6,1) -> 12 U11_1(5,6,5) -> 12 U11_1(5,6,6) -> 12 U11_1(5,6,11) -> 12 U11_1(5,11,1) -> 12 U11_1(5,11,5) -> 12 U11_1(5,11,6) -> 12 U11_1(5,11,11) -> 12 U11_1(6,1,1) -> 12 U11_1(6,1,5) -> 12 U11_1(6,1,6) -> 12 U11_1(6,1,11) -> 12 U11_1(6,5,1) -> 12 U11_1(6,5,5) -> 12 U11_1(6,5,6) -> 12 U11_1(6,5,11) -> 12 U11_1(6,6,1) -> 12 U11_1(6,6,5) -> 12 U11_1(6,6,6) -> 12 U11_1(6,6,11) -> 12 U11_1(6,11,1) -> 12 U11_1(6,11,5) -> 12 U11_1(6,11,6) -> 12 U11_1(6,11,11) -> 12 U11_1(11,1,1) -> 12 U11_1(11,1,5) -> 12 U11_1(11,1,6) -> 12 U11_1(11,1,11) -> 12 U11_1(11,5,1) -> 12 U11_1(11,5,5) -> 12 U11_1(11,5,6) -> 12 U11_1(11,5,11) -> 12 U11_1(11,6,1) -> 12 U11_1(11,6,5) -> 12 U11_1(11,6,6) -> 12 U11_1(11,6,11) -> 12 U11_1(11,11,1) -> 12 U11_1(11,11,5) -> 12 U11_1(11,11,6) -> 12 U11_1(11,11,11) -> 12 U12_0(1,1,1) -> 3 U12_0(1,1,5) -> 3 U12_0(1,1,6) -> 3 U12_0(1,1,11) -> 3 U12_0(1,5,1) -> 3 U12_0(1,5,5) -> 3 U12_0(1,5,6) -> 3 U12_0(1,5,11) -> 3 U12_0(1,6,1) -> 3 U12_0(1,6,5) -> 3 U12_0(1,6,6) -> 3 U12_0(1,6,11) -> 3 U12_0(1,11,1) -> 3 U12_0(1,11,5) -> 3 U12_0(1,11,6) -> 3 U12_0(1,11,11) -> 3 U12_0(5,1,1) -> 3 U12_0(5,1,5) -> 3 U12_0(5,1,6) -> 3 U12_0(5,1,11) -> 3 U12_0(5,5,1) -> 3 U12_0(5,5,5) -> 3 U12_0(5,5,6) -> 3 U12_0(5,5,11) -> 3 U12_0(5,6,1) -> 3 U12_0(5,6,5) -> 3 U12_0(5,6,6) -> 3 U12_0(5,6,11) -> 3 U12_0(5,11,1) -> 3 U12_0(5,11,5) -> 3 U12_0(5,11,6) -> 3 U12_0(5,11,11) -> 3 U12_0(6,1,1) -> 3 U12_0(6,1,5) -> 3 U12_0(6,1,6) -> 3 U12_0(6,1,11) -> 3 U12_0(6,5,1) -> 3 U12_0(6,5,5) -> 3 U12_0(6,5,6) -> 3 U12_0(6,5,11) -> 3 U12_0(6,6,1) -> 3 U12_0(6,6,5) -> 3 U12_0(6,6,6) -> 3 U12_0(6,6,11) -> 3 U12_0(6,11,1) -> 3 U12_0(6,11,5) -> 3 U12_0(6,11,6) -> 3 U12_0(6,11,11) -> 3 U12_0(11,1,1) -> 3 U12_0(11,1,5) -> 3 U12_0(11,1,6) -> 3 U12_0(11,1,11) -> 3 U12_0(11,5,1) -> 3 U12_0(11,5,5) -> 3 U12_0(11,5,6) -> 3 U12_0(11,5,11) -> 3 U12_0(11,6,1) -> 3 U12_0(11,6,5) -> 3 U12_0(11,6,6) -> 3 U12_0(11,6,11) -> 3 U12_0(11,11,1) -> 3 U12_0(11,11,5) -> 3 U12_0(11,11,6) -> 3 U12_0(11,11,11) -> 3 U12_1(1,1,1) -> 13 U12_1(1,1,5) -> 13 U12_1(1,1,6) -> 13 U12_1(1,1,11) -> 13 U12_1(1,5,1) -> 13 U12_1(1,5,5) -> 13 U12_1(1,5,6) -> 13 U12_1(1,5,11) -> 13 U12_1(1,6,1) -> 13 U12_1(1,6,5) -> 13 U12_1(1,6,6) -> 13 U12_1(1,6,11) -> 13 U12_1(1,11,1) -> 13 U12_1(1,11,5) -> 13 U12_1(1,11,6) -> 13 U12_1(1,11,11) -> 13 U12_1(5,1,1) -> 13 U12_1(5,1,5) -> 13 U12_1(5,1,6) -> 13 U12_1(5,1,11) -> 13 U12_1(5,5,1) -> 13 U12_1(5,5,5) -> 13 U12_1(5,5,6) -> 13 U12_1(5,5,11) -> 13 U12_1(5,6,1) -> 13 U12_1(5,6,5) -> 13 U12_1(5,6,6) -> 13 U12_1(5,6,11) -> 13 U12_1(5,11,1) -> 13 U12_1(5,11,5) -> 13 U12_1(5,11,6) -> 13 U12_1(5,11,11) -> 13 U12_1(6,1,1) -> 13 U12_1(6,1,5) -> 13 U12_1(6,1,6) -> 13 U12_1(6,1,11) -> 13 U12_1(6,5,1) -> 13 U12_1(6,5,5) -> 13 U12_1(6,5,6) -> 13 U12_1(6,5,11) -> 13 U12_1(6,6,1) -> 13 U12_1(6,6,5) -> 13 U12_1(6,6,6) -> 13 U12_1(6,6,11) -> 13 U12_1(6,11,1) -> 13 U12_1(6,11,5) -> 13 U12_1(6,11,6) -> 13 U12_1(6,11,11) -> 13 U12_1(11,1,1) -> 13 U12_1(11,1,5) -> 13 U12_1(11,1,6) -> 13 U12_1(11,1,11) -> 13 U12_1(11,5,1) -> 13 U12_1(11,5,5) -> 13 U12_1(11,5,6) -> 13 U12_1(11,5,11) -> 13 U12_1(11,6,1) -> 13 U12_1(11,6,5) -> 13 U12_1(11,6,6) -> 13 U12_1(11,6,11) -> 13 U12_1(11,11,1) -> 13 U12_1(11,11,5) -> 13 U12_1(11,11,6) -> 13 U12_1(11,11,11) -> 13 active_0(1) -> 4 active_0(5) -> 4 active_0(6) -> 4 active_0(11) -> 4 active_1(1) -> 17 active_1(5) -> 17 active_1(6) -> 17 active_1(11) -> 17 active_2(15) -> 18 mark_0(1) -> 5 mark_0(5) -> 5 mark_0(6) -> 5 mark_0(11) -> 5 mark_1(12) -> 2 mark_1(12) -> 12 mark_1(13) -> 3 mark_1(13) -> 13 mark_1(14) -> 7 mark_1(14) -> 14 mark_1(16) -> 9 mark_1(16) -> 16 ok_0(1) -> 6 ok_0(5) -> 6 ok_0(6) -> 6 ok_0(11) -> 6 ok_1(12) -> 2 ok_1(12) -> 12 ok_1(13) -> 3 ok_1(13) -> 13 ok_1(14) -> 7 ok_1(14) -> 14 ok_1(15) -> 8 ok_1(15) -> 17 ok_1(16) -> 9 ok_1(16) -> 16 plus_0(1,1) -> 7 plus_0(1,5) -> 7 plus_0(1,6) -> 7 plus_0(1,11) -> 7 plus_0(5,1) -> 7 plus_0(5,5) -> 7 plus_0(5,6) -> 7 plus_0(5,11) -> 7 plus_0(6,1) -> 7 plus_0(6,5) -> 7 plus_0(6,6) -> 7 plus_0(6,11) -> 7 plus_0(11,1) -> 7 plus_0(11,5) -> 7 plus_0(11,6) -> 7 plus_0(11,11) -> 7 plus_1(1,1) -> 14 plus_1(1,5) -> 14 plus_1(1,6) -> 14 plus_1(1,11) -> 14 plus_1(5,1) -> 14 plus_1(5,5) -> 14 plus_1(5,6) -> 14 plus_1(5,11) -> 14 plus_1(6,1) -> 14 plus_1(6,5) -> 14 plus_1(6,6) -> 14 plus_1(6,11) -> 14 plus_1(11,1) -> 14 plus_1(11,5) -> 14 plus_1(11,6) -> 14 plus_1(11,11) -> 14 proper_0(1) -> 8 proper_0(5) -> 8 proper_0(6) -> 8 proper_0(11) -> 8 proper_1(1) -> 17 proper_1(5) -> 17 proper_1(6) -> 17 proper_1(11) -> 17 s_0(1) -> 9 s_0(5) -> 9 s_0(6) -> 9 s_0(11) -> 9 s_1(1) -> 16 s_1(5) -> 16 s_1(6) -> 16 s_1(11) -> 16 top_0(1) -> 10 top_0(5) -> 10 top_0(6) -> 10 top_0(11) -> 10 top_1(17) -> 10 top_2(18) -> 10 tt_0() -> 11 tt_1() -> 15 ** Step 1.b:2: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(plus(X1,X2)) -> plus(X1,active(X2)) active(plus(X1,X2)) -> plus(active(X1),X2) active(s(X)) -> s(active(X)) 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(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) 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: {U11/3,U12/3,active/1,plus/2,proper/1,s/1,top/1} / {0/0,mark/1,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {U11,U12,active,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))