/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: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U12(mark(X)) -> mark(U12(X)) U12(ok(X)) -> ok(U12(X)) __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) active(U11(X)) -> U11(active(X)) active(U11(tt())) -> mark(U12(tt())) active(U12(X)) -> U12(active(X)) active(U12(tt())) -> mark(tt()) active(__(X,nil())) -> mark(X) active(__(X1,X2)) -> __(X1,active(X2)) active(__(X1,X2)) -> __(active(X1),X2) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil(),X)) -> mark(X) active(isNePal(X)) -> isNePal(active(X)) active(isNePal(__(I,__(P,I)))) -> mark(U11(tt())) isNePal(mark(X)) -> mark(isNePal(X)) isNePal(ok(X)) -> ok(isNePal(X)) proper(U11(X)) -> U11(proper(X)) proper(U12(X)) -> U12(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isNePal(X)) -> isNePal(proper(X)) proper(nil()) -> ok(nil()) proper(tt()) -> ok(tt()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {U11/1,U12/1,__/2,active/1,isNePal/1,proper/1,top/1} / {mark/1,nil/0,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {U11,U12,__,active,isNePal,proper,top} and constructors {mark,nil ,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(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U12(mark(X)) -> mark(U12(X)) U12(ok(X)) -> ok(U12(X)) __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) active(U11(X)) -> U11(active(X)) active(U11(tt())) -> mark(U12(tt())) active(U12(X)) -> U12(active(X)) active(U12(tt())) -> mark(tt()) active(__(X,nil())) -> mark(X) active(__(X1,X2)) -> __(X1,active(X2)) active(__(X1,X2)) -> __(active(X1),X2) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil(),X)) -> mark(X) active(isNePal(X)) -> isNePal(active(X)) active(isNePal(__(I,__(P,I)))) -> mark(U11(tt())) isNePal(mark(X)) -> mark(isNePal(X)) isNePal(ok(X)) -> ok(isNePal(X)) proper(U11(X)) -> U11(proper(X)) proper(U12(X)) -> U12(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isNePal(X)) -> isNePal(proper(X)) proper(nil()) -> ok(nil()) proper(tt()) -> ok(tt()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {U11/1,U12/1,__/2,active/1,isNePal/1,proper/1,top/1} / {mark/1,nil/0,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {U11,U12,__,active,isNePal,proper,top} and constructors {mark,nil ,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(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U12(mark(X)) -> mark(U12(X)) U12(ok(X)) -> ok(U12(X)) __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) active(U11(X)) -> U11(active(X)) active(U11(tt())) -> mark(U12(tt())) active(U12(X)) -> U12(active(X)) active(U12(tt())) -> mark(tt()) active(__(X,nil())) -> mark(X) active(__(X1,X2)) -> __(X1,active(X2)) active(__(X1,X2)) -> __(active(X1),X2) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil(),X)) -> mark(X) active(isNePal(X)) -> isNePal(active(X)) active(isNePal(__(I,__(P,I)))) -> mark(U11(tt())) isNePal(mark(X)) -> mark(isNePal(X)) isNePal(ok(X)) -> ok(isNePal(X)) proper(U11(X)) -> U11(proper(X)) proper(U12(X)) -> U12(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isNePal(X)) -> isNePal(proper(X)) proper(nil()) -> ok(nil()) proper(tt()) -> ok(tt()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {U11/1,U12/1,__/2,active/1,isNePal/1,proper/1,top/1} / {mark/1,nil/0,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {U11,U12,__,active,isNePal,proper,top} and constructors {mark,nil ,ok,tt} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: U11(x){x -> mark(x)} = U11(mark(x)) ->^+ mark(U11(x)) = C[U11(x) = U11(x){}] ** Step 1.b:1: Bounds. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U12(mark(X)) -> mark(U12(X)) U12(ok(X)) -> ok(U12(X)) __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) active(U11(X)) -> U11(active(X)) active(U11(tt())) -> mark(U12(tt())) active(U12(X)) -> U12(active(X)) active(U12(tt())) -> mark(tt()) active(__(X,nil())) -> mark(X) active(__(X1,X2)) -> __(X1,active(X2)) active(__(X1,X2)) -> __(active(X1),X2) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil(),X)) -> mark(X) active(isNePal(X)) -> isNePal(active(X)) active(isNePal(__(I,__(P,I)))) -> mark(U11(tt())) isNePal(mark(X)) -> mark(isNePal(X)) isNePal(ok(X)) -> ok(isNePal(X)) proper(U11(X)) -> U11(proper(X)) proper(U12(X)) -> U12(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isNePal(X)) -> isNePal(proper(X)) proper(nil()) -> ok(nil()) proper(tt()) -> ok(tt()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {U11/1,U12/1,__/2,active/1,isNePal/1,proper/1,top/1} / {mark/1,nil/0,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {U11,U12,__,active,isNePal,proper,top} and constructors {mark,nil ,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. U11_0(6) -> 1 U11_0(7) -> 1 U11_0(8) -> 1 U11_0(11) -> 1 U11_1(6) -> 12 U11_1(7) -> 12 U11_1(8) -> 12 U11_1(11) -> 12 U12_0(6) -> 2 U12_0(7) -> 2 U12_0(8) -> 2 U12_0(11) -> 2 U12_1(6) -> 13 U12_1(7) -> 13 U12_1(8) -> 13 U12_1(11) -> 13 ___0(6,6) -> 3 ___0(6,7) -> 3 ___0(6,8) -> 3 ___0(6,11) -> 3 ___0(7,6) -> 3 ___0(7,7) -> 3 ___0(7,8) -> 3 ___0(7,11) -> 3 ___0(8,6) -> 3 ___0(8,7) -> 3 ___0(8,8) -> 3 ___0(8,11) -> 3 ___0(11,6) -> 3 ___0(11,7) -> 3 ___0(11,8) -> 3 ___0(11,11) -> 3 ___1(6,6) -> 14 ___1(6,7) -> 14 ___1(6,8) -> 14 ___1(6,11) -> 14 ___1(7,6) -> 14 ___1(7,7) -> 14 ___1(7,8) -> 14 ___1(7,11) -> 14 ___1(8,6) -> 14 ___1(8,7) -> 14 ___1(8,8) -> 14 ___1(8,11) -> 14 ___1(11,6) -> 14 ___1(11,7) -> 14 ___1(11,8) -> 14 ___1(11,11) -> 14 active_0(6) -> 4 active_0(7) -> 4 active_0(8) -> 4 active_0(11) -> 4 active_1(6) -> 17 active_1(7) -> 17 active_1(8) -> 17 active_1(11) -> 17 active_2(16) -> 18 isNePal_0(6) -> 5 isNePal_0(7) -> 5 isNePal_0(8) -> 5 isNePal_0(11) -> 5 isNePal_1(6) -> 15 isNePal_1(7) -> 15 isNePal_1(8) -> 15 isNePal_1(11) -> 15 mark_0(6) -> 6 mark_0(7) -> 6 mark_0(8) -> 6 mark_0(11) -> 6 mark_1(12) -> 1 mark_1(12) -> 12 mark_1(13) -> 2 mark_1(13) -> 13 mark_1(14) -> 3 mark_1(14) -> 14 mark_1(15) -> 5 mark_1(15) -> 15 nil_0() -> 7 nil_1() -> 16 ok_0(6) -> 8 ok_0(7) -> 8 ok_0(8) -> 8 ok_0(11) -> 8 ok_1(12) -> 1 ok_1(12) -> 12 ok_1(13) -> 2 ok_1(13) -> 13 ok_1(14) -> 3 ok_1(14) -> 14 ok_1(15) -> 5 ok_1(15) -> 15 ok_1(16) -> 9 ok_1(16) -> 17 proper_0(6) -> 9 proper_0(7) -> 9 proper_0(8) -> 9 proper_0(11) -> 9 proper_1(6) -> 17 proper_1(7) -> 17 proper_1(8) -> 17 proper_1(11) -> 17 top_0(6) -> 10 top_0(7) -> 10 top_0(8) -> 10 top_0(11) -> 10 top_1(17) -> 10 top_2(18) -> 10 tt_0() -> 11 tt_1() -> 16 ** Step 1.b:2: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U12(mark(X)) -> mark(U12(X)) U12(ok(X)) -> ok(U12(X)) __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) active(U11(X)) -> U11(active(X)) active(U11(tt())) -> mark(U12(tt())) active(U12(X)) -> U12(active(X)) active(U12(tt())) -> mark(tt()) active(__(X,nil())) -> mark(X) active(__(X1,X2)) -> __(X1,active(X2)) active(__(X1,X2)) -> __(active(X1),X2) active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(nil(),X)) -> mark(X) active(isNePal(X)) -> isNePal(active(X)) active(isNePal(__(I,__(P,I)))) -> mark(U11(tt())) isNePal(mark(X)) -> mark(isNePal(X)) isNePal(ok(X)) -> ok(isNePal(X)) proper(U11(X)) -> U11(proper(X)) proper(U12(X)) -> U12(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isNePal(X)) -> isNePal(proper(X)) proper(nil()) -> ok(nil()) proper(tt()) -> ok(tt()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {U11/1,U12/1,__/2,active/1,isNePal/1,proper/1,top/1} / {mark/1,nil/0,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {U11,U12,__,active,isNePal,proper,top} and constructors {mark,nil ,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))