/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: __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) 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(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(isNePal(X)) -> isNePal(active(X)) active(isNePal(__(I,__(P,I)))) -> mark(tt()) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) isNePal(ok(X)) -> ok(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(and(X1,X2)) -> and(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: {__/2,active/1,and/2,isNePal/1,proper/1,top/1} / {mark/1,nil/0,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {__,active,and,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: __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) 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(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(isNePal(X)) -> isNePal(active(X)) active(isNePal(__(I,__(P,I)))) -> mark(tt()) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) isNePal(ok(X)) -> ok(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(and(X1,X2)) -> and(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: {__/2,active/1,and/2,isNePal/1,proper/1,top/1} / {mark/1,nil/0,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {__,active,and,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: __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) 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(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(isNePal(X)) -> isNePal(active(X)) active(isNePal(__(I,__(P,I)))) -> mark(tt()) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) isNePal(ok(X)) -> ok(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(and(X1,X2)) -> and(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: {__/2,active/1,and/2,isNePal/1,proper/1,top/1} / {mark/1,nil/0,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {__,active,and,isNePal,proper,top} and constructors {mark,nil,ok ,tt} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: __(x,y){y -> mark(y)} = __(x,mark(y)) ->^+ mark(__(x,y)) = C[__(x,y) = __(x,y){}] ** Step 1.b:1: Bounds. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) 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(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(isNePal(X)) -> isNePal(active(X)) active(isNePal(__(I,__(P,I)))) -> mark(tt()) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) isNePal(ok(X)) -> ok(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(and(X1,X2)) -> and(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: {__/2,active/1,and/2,isNePal/1,proper/1,top/1} / {mark/1,nil/0,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {__,active,and,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. ___0(5,5) -> 1 ___0(5,6) -> 1 ___0(5,7) -> 1 ___0(5,10) -> 1 ___0(6,5) -> 1 ___0(6,6) -> 1 ___0(6,7) -> 1 ___0(6,10) -> 1 ___0(7,5) -> 1 ___0(7,6) -> 1 ___0(7,7) -> 1 ___0(7,10) -> 1 ___0(10,5) -> 1 ___0(10,6) -> 1 ___0(10,7) -> 1 ___0(10,10) -> 1 ___1(5,5) -> 11 ___1(5,6) -> 11 ___1(5,7) -> 11 ___1(5,10) -> 11 ___1(6,5) -> 11 ___1(6,6) -> 11 ___1(6,7) -> 11 ___1(6,10) -> 11 ___1(7,5) -> 11 ___1(7,6) -> 11 ___1(7,7) -> 11 ___1(7,10) -> 11 ___1(10,5) -> 11 ___1(10,6) -> 11 ___1(10,7) -> 11 ___1(10,10) -> 11 active_0(5) -> 2 active_0(6) -> 2 active_0(7) -> 2 active_0(10) -> 2 active_1(5) -> 15 active_1(6) -> 15 active_1(7) -> 15 active_1(10) -> 15 active_2(14) -> 16 and_0(5,5) -> 3 and_0(5,6) -> 3 and_0(5,7) -> 3 and_0(5,10) -> 3 and_0(6,5) -> 3 and_0(6,6) -> 3 and_0(6,7) -> 3 and_0(6,10) -> 3 and_0(7,5) -> 3 and_0(7,6) -> 3 and_0(7,7) -> 3 and_0(7,10) -> 3 and_0(10,5) -> 3 and_0(10,6) -> 3 and_0(10,7) -> 3 and_0(10,10) -> 3 and_1(5,5) -> 12 and_1(5,6) -> 12 and_1(5,7) -> 12 and_1(5,10) -> 12 and_1(6,5) -> 12 and_1(6,6) -> 12 and_1(6,7) -> 12 and_1(6,10) -> 12 and_1(7,5) -> 12 and_1(7,6) -> 12 and_1(7,7) -> 12 and_1(7,10) -> 12 and_1(10,5) -> 12 and_1(10,6) -> 12 and_1(10,7) -> 12 and_1(10,10) -> 12 isNePal_0(5) -> 4 isNePal_0(6) -> 4 isNePal_0(7) -> 4 isNePal_0(10) -> 4 isNePal_1(5) -> 13 isNePal_1(6) -> 13 isNePal_1(7) -> 13 isNePal_1(10) -> 13 mark_0(5) -> 5 mark_0(6) -> 5 mark_0(7) -> 5 mark_0(10) -> 5 mark_1(11) -> 1 mark_1(11) -> 11 mark_1(12) -> 3 mark_1(12) -> 12 mark_1(13) -> 4 mark_1(13) -> 13 nil_0() -> 6 nil_1() -> 14 ok_0(5) -> 7 ok_0(6) -> 7 ok_0(7) -> 7 ok_0(10) -> 7 ok_1(11) -> 1 ok_1(11) -> 11 ok_1(12) -> 3 ok_1(12) -> 12 ok_1(13) -> 4 ok_1(13) -> 13 ok_1(14) -> 8 ok_1(14) -> 15 proper_0(5) -> 8 proper_0(6) -> 8 proper_0(7) -> 8 proper_0(10) -> 8 proper_1(5) -> 15 proper_1(6) -> 15 proper_1(7) -> 15 proper_1(10) -> 15 top_0(5) -> 9 top_0(6) -> 9 top_0(7) -> 9 top_0(10) -> 9 top_1(15) -> 9 top_2(16) -> 9 tt_0() -> 10 tt_1() -> 14 ** Step 1.b:2: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: __(X1,mark(X2)) -> mark(__(X1,X2)) __(mark(X1),X2) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) 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(and(X1,X2)) -> and(active(X1),X2) active(and(tt(),X)) -> mark(X) active(isNePal(X)) -> isNePal(active(X)) active(isNePal(__(I,__(P,I)))) -> mark(tt()) and(mark(X1),X2) -> mark(and(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isNePal(mark(X)) -> mark(isNePal(X)) isNePal(ok(X)) -> ok(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(and(X1,X2)) -> and(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: {__/2,active/1,and/2,isNePal/1,proper/1,top/1} / {mark/1,nil/0,ok/1,tt/0} - Obligation: runtime complexity wrt. defined symbols {__,active,and,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))