/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) -> mark(U11(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U11(tt(),L)) -> mark(U12(tt(),L)) active(U12(X1,X2)) -> U12(active(X1),X2) active(U12(tt(),L)) -> mark(s(length(L))) active(cons(X1,X2)) -> cons(active(X1),X2) active(length(X)) -> length(active(X)) active(length(cons(N,L))) -> mark(U11(tt(),L)) active(length(nil())) -> mark(0()) active(s(X)) -> s(active(X)) active(zeros()) -> mark(cons(0(),zeros())) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) length(mark(X)) -> mark(length(X)) length(ok(X)) -> ok(length(X)) proper(0()) -> ok(0()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(length(X)) -> length(proper(X)) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) proper(tt()) -> ok(tt()) proper(zeros()) -> ok(zeros()) 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: {U11/2,U12/2,active/1,cons/2,length/1,proper/1,s/1,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0} - Obligation: runtime complexity wrt. defined symbols {U11,U12,active,cons,length,proper,s,top} and constructors {0,mark ,nil,ok,tt,zeros} + 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) -> mark(U11(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U11(tt(),L)) -> mark(U12(tt(),L)) active(U12(X1,X2)) -> U12(active(X1),X2) active(U12(tt(),L)) -> mark(s(length(L))) active(cons(X1,X2)) -> cons(active(X1),X2) active(length(X)) -> length(active(X)) active(length(cons(N,L))) -> mark(U11(tt(),L)) active(length(nil())) -> mark(0()) active(s(X)) -> s(active(X)) active(zeros()) -> mark(cons(0(),zeros())) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) length(mark(X)) -> mark(length(X)) length(ok(X)) -> ok(length(X)) proper(0()) -> ok(0()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(length(X)) -> length(proper(X)) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) proper(tt()) -> ok(tt()) proper(zeros()) -> ok(zeros()) 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: {U11/2,U12/2,active/1,cons/2,length/1,proper/1,s/1,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0} - Obligation: runtime complexity wrt. defined symbols {U11,U12,active,cons,length,proper,s,top} and constructors {0,mark ,nil,ok,tt,zeros} + 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) -> mark(U11(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U11(tt(),L)) -> mark(U12(tt(),L)) active(U12(X1,X2)) -> U12(active(X1),X2) active(U12(tt(),L)) -> mark(s(length(L))) active(cons(X1,X2)) -> cons(active(X1),X2) active(length(X)) -> length(active(X)) active(length(cons(N,L))) -> mark(U11(tt(),L)) active(length(nil())) -> mark(0()) active(s(X)) -> s(active(X)) active(zeros()) -> mark(cons(0(),zeros())) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) length(mark(X)) -> mark(length(X)) length(ok(X)) -> ok(length(X)) proper(0()) -> ok(0()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(length(X)) -> length(proper(X)) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) proper(tt()) -> ok(tt()) proper(zeros()) -> ok(zeros()) 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: {U11/2,U12/2,active/1,cons/2,length/1,proper/1,s/1,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0} - Obligation: runtime complexity wrt. defined symbols {U11,U12,active,cons,length,proper,s,top} and constructors {0,mark ,nil,ok,tt,zeros} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: U11(x,y){x -> mark(x)} = U11(mark(x),y) ->^+ mark(U11(x,y)) = C[U11(x,y) = U11(x,y){}] ** Step 1.b:1: Bounds. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: U11(mark(X1),X2) -> mark(U11(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U11(tt(),L)) -> mark(U12(tt(),L)) active(U12(X1,X2)) -> U12(active(X1),X2) active(U12(tt(),L)) -> mark(s(length(L))) active(cons(X1,X2)) -> cons(active(X1),X2) active(length(X)) -> length(active(X)) active(length(cons(N,L))) -> mark(U11(tt(),L)) active(length(nil())) -> mark(0()) active(s(X)) -> s(active(X)) active(zeros()) -> mark(cons(0(),zeros())) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) length(mark(X)) -> mark(length(X)) length(ok(X)) -> ok(length(X)) proper(0()) -> ok(0()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(length(X)) -> length(proper(X)) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) proper(tt()) -> ok(tt()) proper(zeros()) -> ok(zeros()) 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: {U11/2,U12/2,active/1,cons/2,length/1,proper/1,s/1,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0} - Obligation: runtime complexity wrt. defined symbols {U11,U12,active,cons,length,proper,s,top} and constructors {0,mark ,nil,ok,tt,zeros} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 5. The enriched problem is compatible with follwoing automaton. 0_0() -> 1 0_1() -> 18 0_2() -> 26 0_3() -> 37 U11_0(1,1) -> 2 U11_0(1,7) -> 2 U11_0(1,8) -> 2 U11_0(1,9) -> 2 U11_0(1,13) -> 2 U11_0(1,14) -> 2 U11_0(7,1) -> 2 U11_0(7,7) -> 2 U11_0(7,8) -> 2 U11_0(7,9) -> 2 U11_0(7,13) -> 2 U11_0(7,14) -> 2 U11_0(8,1) -> 2 U11_0(8,7) -> 2 U11_0(8,8) -> 2 U11_0(8,9) -> 2 U11_0(8,13) -> 2 U11_0(8,14) -> 2 U11_0(9,1) -> 2 U11_0(9,7) -> 2 U11_0(9,8) -> 2 U11_0(9,9) -> 2 U11_0(9,13) -> 2 U11_0(9,14) -> 2 U11_0(13,1) -> 2 U11_0(13,7) -> 2 U11_0(13,8) -> 2 U11_0(13,9) -> 2 U11_0(13,13) -> 2 U11_0(13,14) -> 2 U11_0(14,1) -> 2 U11_0(14,7) -> 2 U11_0(14,8) -> 2 U11_0(14,9) -> 2 U11_0(14,13) -> 2 U11_0(14,14) -> 2 U11_1(1,1) -> 15 U11_1(1,7) -> 15 U11_1(1,8) -> 15 U11_1(1,9) -> 15 U11_1(1,13) -> 15 U11_1(1,14) -> 15 U11_1(7,1) -> 15 U11_1(7,7) -> 15 U11_1(7,8) -> 15 U11_1(7,9) -> 15 U11_1(7,13) -> 15 U11_1(7,14) -> 15 U11_1(8,1) -> 15 U11_1(8,7) -> 15 U11_1(8,8) -> 15 U11_1(8,9) -> 15 U11_1(8,13) -> 15 U11_1(8,14) -> 15 U11_1(9,1) -> 15 U11_1(9,7) -> 15 U11_1(9,8) -> 15 U11_1(9,9) -> 15 U11_1(9,13) -> 15 U11_1(9,14) -> 15 U11_1(13,1) -> 15 U11_1(13,7) -> 15 U11_1(13,8) -> 15 U11_1(13,9) -> 15 U11_1(13,13) -> 15 U11_1(13,14) -> 15 U11_1(14,1) -> 15 U11_1(14,7) -> 15 U11_1(14,8) -> 15 U11_1(14,9) -> 15 U11_1(14,13) -> 15 U11_1(14,14) -> 15 U12_0(1,1) -> 3 U12_0(1,7) -> 3 U12_0(1,8) -> 3 U12_0(1,9) -> 3 U12_0(1,13) -> 3 U12_0(1,14) -> 3 U12_0(7,1) -> 3 U12_0(7,7) -> 3 U12_0(7,8) -> 3 U12_0(7,9) -> 3 U12_0(7,13) -> 3 U12_0(7,14) -> 3 U12_0(8,1) -> 3 U12_0(8,7) -> 3 U12_0(8,8) -> 3 U12_0(8,9) -> 3 U12_0(8,13) -> 3 U12_0(8,14) -> 3 U12_0(9,1) -> 3 U12_0(9,7) -> 3 U12_0(9,8) -> 3 U12_0(9,9) -> 3 U12_0(9,13) -> 3 U12_0(9,14) -> 3 U12_0(13,1) -> 3 U12_0(13,7) -> 3 U12_0(13,8) -> 3 U12_0(13,9) -> 3 U12_0(13,13) -> 3 U12_0(13,14) -> 3 U12_0(14,1) -> 3 U12_0(14,7) -> 3 U12_0(14,8) -> 3 U12_0(14,9) -> 3 U12_0(14,13) -> 3 U12_0(14,14) -> 3 U12_1(1,1) -> 16 U12_1(1,7) -> 16 U12_1(1,8) -> 16 U12_1(1,9) -> 16 U12_1(1,13) -> 16 U12_1(1,14) -> 16 U12_1(7,1) -> 16 U12_1(7,7) -> 16 U12_1(7,8) -> 16 U12_1(7,9) -> 16 U12_1(7,13) -> 16 U12_1(7,14) -> 16 U12_1(8,1) -> 16 U12_1(8,7) -> 16 U12_1(8,8) -> 16 U12_1(8,9) -> 16 U12_1(8,13) -> 16 U12_1(8,14) -> 16 U12_1(9,1) -> 16 U12_1(9,7) -> 16 U12_1(9,8) -> 16 U12_1(9,9) -> 16 U12_1(9,13) -> 16 U12_1(9,14) -> 16 U12_1(13,1) -> 16 U12_1(13,7) -> 16 U12_1(13,8) -> 16 U12_1(13,9) -> 16 U12_1(13,13) -> 16 U12_1(13,14) -> 16 U12_1(14,1) -> 16 U12_1(14,7) -> 16 U12_1(14,8) -> 16 U12_1(14,9) -> 16 U12_1(14,13) -> 16 U12_1(14,14) -> 16 active_0(1) -> 4 active_0(7) -> 4 active_0(8) -> 4 active_0(9) -> 4 active_0(13) -> 4 active_0(14) -> 4 active_1(1) -> 23 active_1(7) -> 23 active_1(8) -> 23 active_1(9) -> 23 active_1(13) -> 23 active_1(14) -> 23 active_2(18) -> 24 active_2(19) -> 24 active_3(32) -> 31 active_4(26) -> 36 active_4(30) -> 36 active_4(38) -> 39 active_5(37) -> 40 cons_0(1,1) -> 5 cons_0(1,7) -> 5 cons_0(1,8) -> 5 cons_0(1,9) -> 5 cons_0(1,13) -> 5 cons_0(1,14) -> 5 cons_0(7,1) -> 5 cons_0(7,7) -> 5 cons_0(7,8) -> 5 cons_0(7,9) -> 5 cons_0(7,13) -> 5 cons_0(7,14) -> 5 cons_0(8,1) -> 5 cons_0(8,7) -> 5 cons_0(8,8) -> 5 cons_0(8,9) -> 5 cons_0(8,13) -> 5 cons_0(8,14) -> 5 cons_0(9,1) -> 5 cons_0(9,7) -> 5 cons_0(9,8) -> 5 cons_0(9,9) -> 5 cons_0(9,13) -> 5 cons_0(9,14) -> 5 cons_0(13,1) -> 5 cons_0(13,7) -> 5 cons_0(13,8) -> 5 cons_0(13,9) -> 5 cons_0(13,13) -> 5 cons_0(13,14) -> 5 cons_0(14,1) -> 5 cons_0(14,7) -> 5 cons_0(14,8) -> 5 cons_0(14,9) -> 5 cons_0(14,13) -> 5 cons_0(14,14) -> 5 cons_1(1,1) -> 20 cons_1(1,7) -> 20 cons_1(1,8) -> 20 cons_1(1,9) -> 20 cons_1(1,13) -> 20 cons_1(1,14) -> 20 cons_1(7,1) -> 20 cons_1(7,7) -> 20 cons_1(7,8) -> 20 cons_1(7,9) -> 20 cons_1(7,13) -> 20 cons_1(7,14) -> 20 cons_1(8,1) -> 20 cons_1(8,7) -> 20 cons_1(8,8) -> 20 cons_1(8,9) -> 20 cons_1(8,13) -> 20 cons_1(8,14) -> 20 cons_1(9,1) -> 20 cons_1(9,7) -> 20 cons_1(9,8) -> 20 cons_1(9,9) -> 20 cons_1(9,13) -> 20 cons_1(9,14) -> 20 cons_1(13,1) -> 20 cons_1(13,7) -> 20 cons_1(13,8) -> 20 cons_1(13,9) -> 20 cons_1(13,13) -> 20 cons_1(13,14) -> 20 cons_1(14,1) -> 20 cons_1(14,7) -> 20 cons_1(14,8) -> 20 cons_1(14,9) -> 20 cons_1(14,13) -> 20 cons_1(14,14) -> 20 cons_1(18,19) -> 17 cons_2(26,27) -> 25 cons_2(28,29) -> 24 cons_3(26,27) -> 32 cons_3(30,27) -> 32 cons_3(33,34) -> 31 cons_4(36,27) -> 31 cons_4(37,35) -> 38 cons_5(40,35) -> 39 length_0(1) -> 6 length_0(7) -> 6 length_0(8) -> 6 length_0(9) -> 6 length_0(13) -> 6 length_0(14) -> 6 length_1(1) -> 21 length_1(7) -> 21 length_1(8) -> 21 length_1(9) -> 21 length_1(13) -> 21 length_1(14) -> 21 mark_0(1) -> 7 mark_0(7) -> 7 mark_0(8) -> 7 mark_0(9) -> 7 mark_0(13) -> 7 mark_0(14) -> 7 mark_1(15) -> 2 mark_1(15) -> 15 mark_1(16) -> 3 mark_1(16) -> 16 mark_1(17) -> 4 mark_1(17) -> 23 mark_1(20) -> 5 mark_1(20) -> 20 mark_1(21) -> 6 mark_1(21) -> 21 mark_1(22) -> 11 mark_1(22) -> 22 mark_2(25) -> 24 nil_0() -> 8 nil_1() -> 18 nil_2() -> 30 ok_0(1) -> 9 ok_0(7) -> 9 ok_0(8) -> 9 ok_0(9) -> 9 ok_0(13) -> 9 ok_0(14) -> 9 ok_1(15) -> 2 ok_1(15) -> 15 ok_1(16) -> 3 ok_1(16) -> 16 ok_1(18) -> 10 ok_1(18) -> 23 ok_1(19) -> 10 ok_1(19) -> 23 ok_1(20) -> 5 ok_1(20) -> 20 ok_1(21) -> 6 ok_1(21) -> 21 ok_1(22) -> 11 ok_1(22) -> 22 ok_2(26) -> 28 ok_2(27) -> 29 ok_2(30) -> 28 ok_3(32) -> 24 ok_3(35) -> 34 ok_3(37) -> 33 ok_4(38) -> 31 proper_0(1) -> 10 proper_0(7) -> 10 proper_0(8) -> 10 proper_0(9) -> 10 proper_0(13) -> 10 proper_0(14) -> 10 proper_1(1) -> 23 proper_1(7) -> 23 proper_1(8) -> 23 proper_1(9) -> 23 proper_1(13) -> 23 proper_1(14) -> 23 proper_2(17) -> 24 proper_2(18) -> 28 proper_2(19) -> 29 proper_3(25) -> 31 proper_3(26) -> 33 proper_3(27) -> 34 s_0(1) -> 11 s_0(7) -> 11 s_0(8) -> 11 s_0(9) -> 11 s_0(13) -> 11 s_0(14) -> 11 s_1(1) -> 22 s_1(7) -> 22 s_1(8) -> 22 s_1(9) -> 22 s_1(13) -> 22 s_1(14) -> 22 top_0(1) -> 12 top_0(7) -> 12 top_0(8) -> 12 top_0(9) -> 12 top_0(13) -> 12 top_0(14) -> 12 top_1(23) -> 12 top_2(24) -> 12 top_3(31) -> 12 top_4(39) -> 12 tt_0() -> 13 tt_1() -> 18 tt_2() -> 30 zeros_0() -> 14 zeros_1() -> 19 zeros_2() -> 27 zeros_3() -> 35 ** Step 1.b:2: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: U11(mark(X1),X2) -> mark(U11(X1,X2)) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(mark(X1),X2) -> mark(U12(X1,X2)) U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U11(tt(),L)) -> mark(U12(tt(),L)) active(U12(X1,X2)) -> U12(active(X1),X2) active(U12(tt(),L)) -> mark(s(length(L))) active(cons(X1,X2)) -> cons(active(X1),X2) active(length(X)) -> length(active(X)) active(length(cons(N,L))) -> mark(U11(tt(),L)) active(length(nil())) -> mark(0()) active(s(X)) -> s(active(X)) active(zeros()) -> mark(cons(0(),zeros())) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) length(mark(X)) -> mark(length(X)) length(ok(X)) -> ok(length(X)) proper(0()) -> ok(0()) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(length(X)) -> length(proper(X)) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) proper(tt()) -> ok(tt()) proper(zeros()) -> ok(zeros()) 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: {U11/2,U12/2,active/1,cons/2,length/1,proper/1,s/1,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0} - Obligation: runtime complexity wrt. defined symbols {U11,U12,active,cons,length,proper,s,top} and constructors {0,mark ,nil,ok,tt,zeros} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))