/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(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(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(tt()) active(U21(X1,X2)) -> U21(active(X1),X2) active(U21(tt(),V2)) -> mark(U22(isList(V2))) active(U22(X)) -> U22(active(X)) active(U22(tt())) -> mark(tt()) active(U31(X)) -> U31(active(X)) active(U31(tt())) -> mark(tt()) active(U41(X1,X2)) -> U41(active(X1),X2) active(U41(tt(),V2)) -> mark(U42(isNeList(V2))) active(U42(X)) -> U42(active(X)) active(U42(tt())) -> mark(tt()) active(U51(X1,X2)) -> U51(active(X1),X2) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U52(X)) -> U52(active(X)) active(U52(tt())) -> mark(tt()) active(U61(X)) -> U61(active(X)) active(U61(tt())) -> mark(tt()) active(U71(X1,X2)) -> U71(active(X1),X2) active(U71(tt(),P)) -> mark(U72(isPal(P))) active(U72(X)) -> U72(active(X)) active(U72(tt())) -> mark(tt()) active(U81(X)) -> U81(active(X)) active(U81(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(isList(V)) -> mark(U11(isNeList(V))) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil())) -> mark(tt()) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isPal(V)) -> mark(U81(isNePal(V))) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(nil()) -> ok(nil()) proper(o()) -> ok(o()) proper(tt()) -> ok(tt()) proper(u()) -> ok(u()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {U11/1,U21/2,U22/1,U31/1,U41/2,U42/1,U51/2,U52/1,U61/1,U71/2,U72/1,U81/1,__/2,active/1,isList/1,isNeList/1 ,isNePal/1,isPal/1,isQid/1,proper/1,top/1} / {a/0,e/0,i/0,mark/1,nil/0,o/0,ok/1,tt/0,u/0} - Obligation: runtime complexity wrt. defined symbols {U11,U21,U22,U31,U41,U42,U51,U52,U61,U71,U72,U81,__,active,isList ,isNeList,isNePal,isPal,isQid,proper,top} and constructors {a,e,i,mark,nil,o,ok,tt,u} + 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)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(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(tt()) active(U21(X1,X2)) -> U21(active(X1),X2) active(U21(tt(),V2)) -> mark(U22(isList(V2))) active(U22(X)) -> U22(active(X)) active(U22(tt())) -> mark(tt()) active(U31(X)) -> U31(active(X)) active(U31(tt())) -> mark(tt()) active(U41(X1,X2)) -> U41(active(X1),X2) active(U41(tt(),V2)) -> mark(U42(isNeList(V2))) active(U42(X)) -> U42(active(X)) active(U42(tt())) -> mark(tt()) active(U51(X1,X2)) -> U51(active(X1),X2) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U52(X)) -> U52(active(X)) active(U52(tt())) -> mark(tt()) active(U61(X)) -> U61(active(X)) active(U61(tt())) -> mark(tt()) active(U71(X1,X2)) -> U71(active(X1),X2) active(U71(tt(),P)) -> mark(U72(isPal(P))) active(U72(X)) -> U72(active(X)) active(U72(tt())) -> mark(tt()) active(U81(X)) -> U81(active(X)) active(U81(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(isList(V)) -> mark(U11(isNeList(V))) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil())) -> mark(tt()) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isPal(V)) -> mark(U81(isNePal(V))) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(nil()) -> ok(nil()) proper(o()) -> ok(o()) proper(tt()) -> ok(tt()) proper(u()) -> ok(u()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {U11/1,U21/2,U22/1,U31/1,U41/2,U42/1,U51/2,U52/1,U61/1,U71/2,U72/1,U81/1,__/2,active/1,isList/1,isNeList/1 ,isNePal/1,isPal/1,isQid/1,proper/1,top/1} / {a/0,e/0,i/0,mark/1,nil/0,o/0,ok/1,tt/0,u/0} - Obligation: runtime complexity wrt. defined symbols {U11,U21,U22,U31,U41,U42,U51,U52,U61,U71,U72,U81,__,active,isList ,isNeList,isNePal,isPal,isQid,proper,top} and constructors {a,e,i,mark,nil,o,ok,tt,u} + 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)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(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(tt()) active(U21(X1,X2)) -> U21(active(X1),X2) active(U21(tt(),V2)) -> mark(U22(isList(V2))) active(U22(X)) -> U22(active(X)) active(U22(tt())) -> mark(tt()) active(U31(X)) -> U31(active(X)) active(U31(tt())) -> mark(tt()) active(U41(X1,X2)) -> U41(active(X1),X2) active(U41(tt(),V2)) -> mark(U42(isNeList(V2))) active(U42(X)) -> U42(active(X)) active(U42(tt())) -> mark(tt()) active(U51(X1,X2)) -> U51(active(X1),X2) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U52(X)) -> U52(active(X)) active(U52(tt())) -> mark(tt()) active(U61(X)) -> U61(active(X)) active(U61(tt())) -> mark(tt()) active(U71(X1,X2)) -> U71(active(X1),X2) active(U71(tt(),P)) -> mark(U72(isPal(P))) active(U72(X)) -> U72(active(X)) active(U72(tt())) -> mark(tt()) active(U81(X)) -> U81(active(X)) active(U81(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(isList(V)) -> mark(U11(isNeList(V))) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil())) -> mark(tt()) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isPal(V)) -> mark(U81(isNePal(V))) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(nil()) -> ok(nil()) proper(o()) -> ok(o()) proper(tt()) -> ok(tt()) proper(u()) -> ok(u()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {U11/1,U21/2,U22/1,U31/1,U41/2,U42/1,U51/2,U52/1,U61/1,U71/2,U72/1,U81/1,__/2,active/1,isList/1,isNeList/1 ,isNePal/1,isPal/1,isQid/1,proper/1,top/1} / {a/0,e/0,i/0,mark/1,nil/0,o/0,ok/1,tt/0,u/0} - Obligation: runtime complexity wrt. defined symbols {U11,U21,U22,U31,U41,U42,U51,U52,U61,U71,U72,U81,__,active,isList ,isNeList,isNePal,isPal,isQid,proper,top} and constructors {a,e,i,mark,nil,o,ok,tt,u} + 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)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(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(tt()) active(U21(X1,X2)) -> U21(active(X1),X2) active(U21(tt(),V2)) -> mark(U22(isList(V2))) active(U22(X)) -> U22(active(X)) active(U22(tt())) -> mark(tt()) active(U31(X)) -> U31(active(X)) active(U31(tt())) -> mark(tt()) active(U41(X1,X2)) -> U41(active(X1),X2) active(U41(tt(),V2)) -> mark(U42(isNeList(V2))) active(U42(X)) -> U42(active(X)) active(U42(tt())) -> mark(tt()) active(U51(X1,X2)) -> U51(active(X1),X2) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U52(X)) -> U52(active(X)) active(U52(tt())) -> mark(tt()) active(U61(X)) -> U61(active(X)) active(U61(tt())) -> mark(tt()) active(U71(X1,X2)) -> U71(active(X1),X2) active(U71(tt(),P)) -> mark(U72(isPal(P))) active(U72(X)) -> U72(active(X)) active(U72(tt())) -> mark(tt()) active(U81(X)) -> U81(active(X)) active(U81(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(isList(V)) -> mark(U11(isNeList(V))) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil())) -> mark(tt()) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isPal(V)) -> mark(U81(isNePal(V))) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(nil()) -> ok(nil()) proper(o()) -> ok(o()) proper(tt()) -> ok(tt()) proper(u()) -> ok(u()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {U11/1,U21/2,U22/1,U31/1,U41/2,U42/1,U51/2,U52/1,U61/1,U71/2,U72/1,U81/1,__/2,active/1,isList/1,isNeList/1 ,isNePal/1,isPal/1,isQid/1,proper/1,top/1} / {a/0,e/0,i/0,mark/1,nil/0,o/0,ok/1,tt/0,u/0} - Obligation: runtime complexity wrt. defined symbols {U11,U21,U22,U31,U41,U42,U51,U52,U61,U71,U72,U81,__,active,isList ,isNeList,isNePal,isPal,isQid,proper,top} and constructors {a,e,i,mark,nil,o,ok,tt,u} + 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(14) -> 1 U11_0(16) -> 1 U11_0(17) -> 1 U11_0(23) -> 1 U11_0(24) -> 1 U11_0(25) -> 1 U11_0(26) -> 1 U11_0(29) -> 1 U11_0(30) -> 1 U11_1(14) -> 31 U11_1(16) -> 31 U11_1(17) -> 31 U11_1(23) -> 31 U11_1(24) -> 31 U11_1(25) -> 31 U11_1(26) -> 31 U11_1(29) -> 31 U11_1(30) -> 31 U21_0(14,14) -> 2 U21_0(14,16) -> 2 U21_0(14,17) -> 2 U21_0(14,23) -> 2 U21_0(14,24) -> 2 U21_0(14,25) -> 2 U21_0(14,26) -> 2 U21_0(14,29) -> 2 U21_0(14,30) -> 2 U21_0(16,14) -> 2 U21_0(16,16) -> 2 U21_0(16,17) -> 2 U21_0(16,23) -> 2 U21_0(16,24) -> 2 U21_0(16,25) -> 2 U21_0(16,26) -> 2 U21_0(16,29) -> 2 U21_0(16,30) -> 2 U21_0(17,14) -> 2 U21_0(17,16) -> 2 U21_0(17,17) -> 2 U21_0(17,23) -> 2 U21_0(17,24) -> 2 U21_0(17,25) -> 2 U21_0(17,26) -> 2 U21_0(17,29) -> 2 U21_0(17,30) -> 2 U21_0(23,14) -> 2 U21_0(23,16) -> 2 U21_0(23,17) -> 2 U21_0(23,23) -> 2 U21_0(23,24) -> 2 U21_0(23,25) -> 2 U21_0(23,26) -> 2 U21_0(23,29) -> 2 U21_0(23,30) -> 2 U21_0(24,14) -> 2 U21_0(24,16) -> 2 U21_0(24,17) -> 2 U21_0(24,23) -> 2 U21_0(24,24) -> 2 U21_0(24,25) -> 2 U21_0(24,26) -> 2 U21_0(24,29) -> 2 U21_0(24,30) -> 2 U21_0(25,14) -> 2 U21_0(25,16) -> 2 U21_0(25,17) -> 2 U21_0(25,23) -> 2 U21_0(25,24) -> 2 U21_0(25,25) -> 2 U21_0(25,26) -> 2 U21_0(25,29) -> 2 U21_0(25,30) -> 2 U21_0(26,14) -> 2 U21_0(26,16) -> 2 U21_0(26,17) -> 2 U21_0(26,23) -> 2 U21_0(26,24) -> 2 U21_0(26,25) -> 2 U21_0(26,26) -> 2 U21_0(26,29) -> 2 U21_0(26,30) -> 2 U21_0(29,14) -> 2 U21_0(29,16) -> 2 U21_0(29,17) -> 2 U21_0(29,23) -> 2 U21_0(29,24) -> 2 U21_0(29,25) -> 2 U21_0(29,26) -> 2 U21_0(29,29) -> 2 U21_0(29,30) -> 2 U21_0(30,14) -> 2 U21_0(30,16) -> 2 U21_0(30,17) -> 2 U21_0(30,23) -> 2 U21_0(30,24) -> 2 U21_0(30,25) -> 2 U21_0(30,26) -> 2 U21_0(30,29) -> 2 U21_0(30,30) -> 2 U21_1(14,14) -> 32 U21_1(14,16) -> 32 U21_1(14,17) -> 32 U21_1(14,23) -> 32 U21_1(14,24) -> 32 U21_1(14,25) -> 32 U21_1(14,26) -> 32 U21_1(14,29) -> 32 U21_1(14,30) -> 32 U21_1(16,14) -> 32 U21_1(16,16) -> 32 U21_1(16,17) -> 32 U21_1(16,23) -> 32 U21_1(16,24) -> 32 U21_1(16,25) -> 32 U21_1(16,26) -> 32 U21_1(16,29) -> 32 U21_1(16,30) -> 32 U21_1(17,14) -> 32 U21_1(17,16) -> 32 U21_1(17,17) -> 32 U21_1(17,23) -> 32 U21_1(17,24) -> 32 U21_1(17,25) -> 32 U21_1(17,26) -> 32 U21_1(17,29) -> 32 U21_1(17,30) -> 32 U21_1(23,14) -> 32 U21_1(23,16) -> 32 U21_1(23,17) -> 32 U21_1(23,23) -> 32 U21_1(23,24) -> 32 U21_1(23,25) -> 32 U21_1(23,26) -> 32 U21_1(23,29) -> 32 U21_1(23,30) -> 32 U21_1(24,14) -> 32 U21_1(24,16) -> 32 U21_1(24,17) -> 32 U21_1(24,23) -> 32 U21_1(24,24) -> 32 U21_1(24,25) -> 32 U21_1(24,26) -> 32 U21_1(24,29) -> 32 U21_1(24,30) -> 32 U21_1(25,14) -> 32 U21_1(25,16) -> 32 U21_1(25,17) -> 32 U21_1(25,23) -> 32 U21_1(25,24) -> 32 U21_1(25,25) -> 32 U21_1(25,26) -> 32 U21_1(25,29) -> 32 U21_1(25,30) -> 32 U21_1(26,14) -> 32 U21_1(26,16) -> 32 U21_1(26,17) -> 32 U21_1(26,23) -> 32 U21_1(26,24) -> 32 U21_1(26,25) -> 32 U21_1(26,26) -> 32 U21_1(26,29) -> 32 U21_1(26,30) -> 32 U21_1(29,14) -> 32 U21_1(29,16) -> 32 U21_1(29,17) -> 32 U21_1(29,23) -> 32 U21_1(29,24) -> 32 U21_1(29,25) -> 32 U21_1(29,26) -> 32 U21_1(29,29) -> 32 U21_1(29,30) -> 32 U21_1(30,14) -> 32 U21_1(30,16) -> 32 U21_1(30,17) -> 32 U21_1(30,23) -> 32 U21_1(30,24) -> 32 U21_1(30,25) -> 32 U21_1(30,26) -> 32 U21_1(30,29) -> 32 U21_1(30,30) -> 32 U22_0(14) -> 3 U22_0(16) -> 3 U22_0(17) -> 3 U22_0(23) -> 3 U22_0(24) -> 3 U22_0(25) -> 3 U22_0(26) -> 3 U22_0(29) -> 3 U22_0(30) -> 3 U22_1(14) -> 33 U22_1(16) -> 33 U22_1(17) -> 33 U22_1(23) -> 33 U22_1(24) -> 33 U22_1(25) -> 33 U22_1(26) -> 33 U22_1(29) -> 33 U22_1(30) -> 33 U31_0(14) -> 4 U31_0(16) -> 4 U31_0(17) -> 4 U31_0(23) -> 4 U31_0(24) -> 4 U31_0(25) -> 4 U31_0(26) -> 4 U31_0(29) -> 4 U31_0(30) -> 4 U31_1(14) -> 34 U31_1(16) -> 34 U31_1(17) -> 34 U31_1(23) -> 34 U31_1(24) -> 34 U31_1(25) -> 34 U31_1(26) -> 34 U31_1(29) -> 34 U31_1(30) -> 34 U41_0(14,14) -> 5 U41_0(14,16) -> 5 U41_0(14,17) -> 5 U41_0(14,23) -> 5 U41_0(14,24) -> 5 U41_0(14,25) -> 5 U41_0(14,26) -> 5 U41_0(14,29) -> 5 U41_0(14,30) -> 5 U41_0(16,14) -> 5 U41_0(16,16) -> 5 U41_0(16,17) -> 5 U41_0(16,23) -> 5 U41_0(16,24) -> 5 U41_0(16,25) -> 5 U41_0(16,26) -> 5 U41_0(16,29) -> 5 U41_0(16,30) -> 5 U41_0(17,14) -> 5 U41_0(17,16) -> 5 U41_0(17,17) -> 5 U41_0(17,23) -> 5 U41_0(17,24) -> 5 U41_0(17,25) -> 5 U41_0(17,26) -> 5 U41_0(17,29) -> 5 U41_0(17,30) -> 5 U41_0(23,14) -> 5 U41_0(23,16) -> 5 U41_0(23,17) -> 5 U41_0(23,23) -> 5 U41_0(23,24) -> 5 U41_0(23,25) -> 5 U41_0(23,26) -> 5 U41_0(23,29) -> 5 U41_0(23,30) -> 5 U41_0(24,14) -> 5 U41_0(24,16) -> 5 U41_0(24,17) -> 5 U41_0(24,23) -> 5 U41_0(24,24) -> 5 U41_0(24,25) -> 5 U41_0(24,26) -> 5 U41_0(24,29) -> 5 U41_0(24,30) -> 5 U41_0(25,14) -> 5 U41_0(25,16) -> 5 U41_0(25,17) -> 5 U41_0(25,23) -> 5 U41_0(25,24) -> 5 U41_0(25,25) -> 5 U41_0(25,26) -> 5 U41_0(25,29) -> 5 U41_0(25,30) -> 5 U41_0(26,14) -> 5 U41_0(26,16) -> 5 U41_0(26,17) -> 5 U41_0(26,23) -> 5 U41_0(26,24) -> 5 U41_0(26,25) -> 5 U41_0(26,26) -> 5 U41_0(26,29) -> 5 U41_0(26,30) -> 5 U41_0(29,14) -> 5 U41_0(29,16) -> 5 U41_0(29,17) -> 5 U41_0(29,23) -> 5 U41_0(29,24) -> 5 U41_0(29,25) -> 5 U41_0(29,26) -> 5 U41_0(29,29) -> 5 U41_0(29,30) -> 5 U41_0(30,14) -> 5 U41_0(30,16) -> 5 U41_0(30,17) -> 5 U41_0(30,23) -> 5 U41_0(30,24) -> 5 U41_0(30,25) -> 5 U41_0(30,26) -> 5 U41_0(30,29) -> 5 U41_0(30,30) -> 5 U41_1(14,14) -> 35 U41_1(14,16) -> 35 U41_1(14,17) -> 35 U41_1(14,23) -> 35 U41_1(14,24) -> 35 U41_1(14,25) -> 35 U41_1(14,26) -> 35 U41_1(14,29) -> 35 U41_1(14,30) -> 35 U41_1(16,14) -> 35 U41_1(16,16) -> 35 U41_1(16,17) -> 35 U41_1(16,23) -> 35 U41_1(16,24) -> 35 U41_1(16,25) -> 35 U41_1(16,26) -> 35 U41_1(16,29) -> 35 U41_1(16,30) -> 35 U41_1(17,14) -> 35 U41_1(17,16) -> 35 U41_1(17,17) -> 35 U41_1(17,23) -> 35 U41_1(17,24) -> 35 U41_1(17,25) -> 35 U41_1(17,26) -> 35 U41_1(17,29) -> 35 U41_1(17,30) -> 35 U41_1(23,14) -> 35 U41_1(23,16) -> 35 U41_1(23,17) -> 35 U41_1(23,23) -> 35 U41_1(23,24) -> 35 U41_1(23,25) -> 35 U41_1(23,26) -> 35 U41_1(23,29) -> 35 U41_1(23,30) -> 35 U41_1(24,14) -> 35 U41_1(24,16) -> 35 U41_1(24,17) -> 35 U41_1(24,23) -> 35 U41_1(24,24) -> 35 U41_1(24,25) -> 35 U41_1(24,26) -> 35 U41_1(24,29) -> 35 U41_1(24,30) -> 35 U41_1(25,14) -> 35 U41_1(25,16) -> 35 U41_1(25,17) -> 35 U41_1(25,23) -> 35 U41_1(25,24) -> 35 U41_1(25,25) -> 35 U41_1(25,26) -> 35 U41_1(25,29) -> 35 U41_1(25,30) -> 35 U41_1(26,14) -> 35 U41_1(26,16) -> 35 U41_1(26,17) -> 35 U41_1(26,23) -> 35 U41_1(26,24) -> 35 U41_1(26,25) -> 35 U41_1(26,26) -> 35 U41_1(26,29) -> 35 U41_1(26,30) -> 35 U41_1(29,14) -> 35 U41_1(29,16) -> 35 U41_1(29,17) -> 35 U41_1(29,23) -> 35 U41_1(29,24) -> 35 U41_1(29,25) -> 35 U41_1(29,26) -> 35 U41_1(29,29) -> 35 U41_1(29,30) -> 35 U41_1(30,14) -> 35 U41_1(30,16) -> 35 U41_1(30,17) -> 35 U41_1(30,23) -> 35 U41_1(30,24) -> 35 U41_1(30,25) -> 35 U41_1(30,26) -> 35 U41_1(30,29) -> 35 U41_1(30,30) -> 35 U42_0(14) -> 6 U42_0(16) -> 6 U42_0(17) -> 6 U42_0(23) -> 6 U42_0(24) -> 6 U42_0(25) -> 6 U42_0(26) -> 6 U42_0(29) -> 6 U42_0(30) -> 6 U42_1(14) -> 36 U42_1(16) -> 36 U42_1(17) -> 36 U42_1(23) -> 36 U42_1(24) -> 36 U42_1(25) -> 36 U42_1(26) -> 36 U42_1(29) -> 36 U42_1(30) -> 36 U51_0(14,14) -> 7 U51_0(14,16) -> 7 U51_0(14,17) -> 7 U51_0(14,23) -> 7 U51_0(14,24) -> 7 U51_0(14,25) -> 7 U51_0(14,26) -> 7 U51_0(14,29) -> 7 U51_0(14,30) -> 7 U51_0(16,14) -> 7 U51_0(16,16) -> 7 U51_0(16,17) -> 7 U51_0(16,23) -> 7 U51_0(16,24) -> 7 U51_0(16,25) -> 7 U51_0(16,26) -> 7 U51_0(16,29) -> 7 U51_0(16,30) -> 7 U51_0(17,14) -> 7 U51_0(17,16) -> 7 U51_0(17,17) -> 7 U51_0(17,23) -> 7 U51_0(17,24) -> 7 U51_0(17,25) -> 7 U51_0(17,26) -> 7 U51_0(17,29) -> 7 U51_0(17,30) -> 7 U51_0(23,14) -> 7 U51_0(23,16) -> 7 U51_0(23,17) -> 7 U51_0(23,23) -> 7 U51_0(23,24) -> 7 U51_0(23,25) -> 7 U51_0(23,26) -> 7 U51_0(23,29) -> 7 U51_0(23,30) -> 7 U51_0(24,14) -> 7 U51_0(24,16) -> 7 U51_0(24,17) -> 7 U51_0(24,23) -> 7 U51_0(24,24) -> 7 U51_0(24,25) -> 7 U51_0(24,26) -> 7 U51_0(24,29) -> 7 U51_0(24,30) -> 7 U51_0(25,14) -> 7 U51_0(25,16) -> 7 U51_0(25,17) -> 7 U51_0(25,23) -> 7 U51_0(25,24) -> 7 U51_0(25,25) -> 7 U51_0(25,26) -> 7 U51_0(25,29) -> 7 U51_0(25,30) -> 7 U51_0(26,14) -> 7 U51_0(26,16) -> 7 U51_0(26,17) -> 7 U51_0(26,23) -> 7 U51_0(26,24) -> 7 U51_0(26,25) -> 7 U51_0(26,26) -> 7 U51_0(26,29) -> 7 U51_0(26,30) -> 7 U51_0(29,14) -> 7 U51_0(29,16) -> 7 U51_0(29,17) -> 7 U51_0(29,23) -> 7 U51_0(29,24) -> 7 U51_0(29,25) -> 7 U51_0(29,26) -> 7 U51_0(29,29) -> 7 U51_0(29,30) -> 7 U51_0(30,14) -> 7 U51_0(30,16) -> 7 U51_0(30,17) -> 7 U51_0(30,23) -> 7 U51_0(30,24) -> 7 U51_0(30,25) -> 7 U51_0(30,26) -> 7 U51_0(30,29) -> 7 U51_0(30,30) -> 7 U51_1(14,14) -> 37 U51_1(14,16) -> 37 U51_1(14,17) -> 37 U51_1(14,23) -> 37 U51_1(14,24) -> 37 U51_1(14,25) -> 37 U51_1(14,26) -> 37 U51_1(14,29) -> 37 U51_1(14,30) -> 37 U51_1(16,14) -> 37 U51_1(16,16) -> 37 U51_1(16,17) -> 37 U51_1(16,23) -> 37 U51_1(16,24) -> 37 U51_1(16,25) -> 37 U51_1(16,26) -> 37 U51_1(16,29) -> 37 U51_1(16,30) -> 37 U51_1(17,14) -> 37 U51_1(17,16) -> 37 U51_1(17,17) -> 37 U51_1(17,23) -> 37 U51_1(17,24) -> 37 U51_1(17,25) -> 37 U51_1(17,26) -> 37 U51_1(17,29) -> 37 U51_1(17,30) -> 37 U51_1(23,14) -> 37 U51_1(23,16) -> 37 U51_1(23,17) -> 37 U51_1(23,23) -> 37 U51_1(23,24) -> 37 U51_1(23,25) -> 37 U51_1(23,26) -> 37 U51_1(23,29) -> 37 U51_1(23,30) -> 37 U51_1(24,14) -> 37 U51_1(24,16) -> 37 U51_1(24,17) -> 37 U51_1(24,23) -> 37 U51_1(24,24) -> 37 U51_1(24,25) -> 37 U51_1(24,26) -> 37 U51_1(24,29) -> 37 U51_1(24,30) -> 37 U51_1(25,14) -> 37 U51_1(25,16) -> 37 U51_1(25,17) -> 37 U51_1(25,23) -> 37 U51_1(25,24) -> 37 U51_1(25,25) -> 37 U51_1(25,26) -> 37 U51_1(25,29) -> 37 U51_1(25,30) -> 37 U51_1(26,14) -> 37 U51_1(26,16) -> 37 U51_1(26,17) -> 37 U51_1(26,23) -> 37 U51_1(26,24) -> 37 U51_1(26,25) -> 37 U51_1(26,26) -> 37 U51_1(26,29) -> 37 U51_1(26,30) -> 37 U51_1(29,14) -> 37 U51_1(29,16) -> 37 U51_1(29,17) -> 37 U51_1(29,23) -> 37 U51_1(29,24) -> 37 U51_1(29,25) -> 37 U51_1(29,26) -> 37 U51_1(29,29) -> 37 U51_1(29,30) -> 37 U51_1(30,14) -> 37 U51_1(30,16) -> 37 U51_1(30,17) -> 37 U51_1(30,23) -> 37 U51_1(30,24) -> 37 U51_1(30,25) -> 37 U51_1(30,26) -> 37 U51_1(30,29) -> 37 U51_1(30,30) -> 37 U52_0(14) -> 8 U52_0(16) -> 8 U52_0(17) -> 8 U52_0(23) -> 8 U52_0(24) -> 8 U52_0(25) -> 8 U52_0(26) -> 8 U52_0(29) -> 8 U52_0(30) -> 8 U52_1(14) -> 38 U52_1(16) -> 38 U52_1(17) -> 38 U52_1(23) -> 38 U52_1(24) -> 38 U52_1(25) -> 38 U52_1(26) -> 38 U52_1(29) -> 38 U52_1(30) -> 38 U61_0(14) -> 9 U61_0(16) -> 9 U61_0(17) -> 9 U61_0(23) -> 9 U61_0(24) -> 9 U61_0(25) -> 9 U61_0(26) -> 9 U61_0(29) -> 9 U61_0(30) -> 9 U61_1(14) -> 39 U61_1(16) -> 39 U61_1(17) -> 39 U61_1(23) -> 39 U61_1(24) -> 39 U61_1(25) -> 39 U61_1(26) -> 39 U61_1(29) -> 39 U61_1(30) -> 39 U71_0(14,14) -> 10 U71_0(14,16) -> 10 U71_0(14,17) -> 10 U71_0(14,23) -> 10 U71_0(14,24) -> 10 U71_0(14,25) -> 10 U71_0(14,26) -> 10 U71_0(14,29) -> 10 U71_0(14,30) -> 10 U71_0(16,14) -> 10 U71_0(16,16) -> 10 U71_0(16,17) -> 10 U71_0(16,23) -> 10 U71_0(16,24) -> 10 U71_0(16,25) -> 10 U71_0(16,26) -> 10 U71_0(16,29) -> 10 U71_0(16,30) -> 10 U71_0(17,14) -> 10 U71_0(17,16) -> 10 U71_0(17,17) -> 10 U71_0(17,23) -> 10 U71_0(17,24) -> 10 U71_0(17,25) -> 10 U71_0(17,26) -> 10 U71_0(17,29) -> 10 U71_0(17,30) -> 10 U71_0(23,14) -> 10 U71_0(23,16) -> 10 U71_0(23,17) -> 10 U71_0(23,23) -> 10 U71_0(23,24) -> 10 U71_0(23,25) -> 10 U71_0(23,26) -> 10 U71_0(23,29) -> 10 U71_0(23,30) -> 10 U71_0(24,14) -> 10 U71_0(24,16) -> 10 U71_0(24,17) -> 10 U71_0(24,23) -> 10 U71_0(24,24) -> 10 U71_0(24,25) -> 10 U71_0(24,26) -> 10 U71_0(24,29) -> 10 U71_0(24,30) -> 10 U71_0(25,14) -> 10 U71_0(25,16) -> 10 U71_0(25,17) -> 10 U71_0(25,23) -> 10 U71_0(25,24) -> 10 U71_0(25,25) -> 10 U71_0(25,26) -> 10 U71_0(25,29) -> 10 U71_0(25,30) -> 10 U71_0(26,14) -> 10 U71_0(26,16) -> 10 U71_0(26,17) -> 10 U71_0(26,23) -> 10 U71_0(26,24) -> 10 U71_0(26,25) -> 10 U71_0(26,26) -> 10 U71_0(26,29) -> 10 U71_0(26,30) -> 10 U71_0(29,14) -> 10 U71_0(29,16) -> 10 U71_0(29,17) -> 10 U71_0(29,23) -> 10 U71_0(29,24) -> 10 U71_0(29,25) -> 10 U71_0(29,26) -> 10 U71_0(29,29) -> 10 U71_0(29,30) -> 10 U71_0(30,14) -> 10 U71_0(30,16) -> 10 U71_0(30,17) -> 10 U71_0(30,23) -> 10 U71_0(30,24) -> 10 U71_0(30,25) -> 10 U71_0(30,26) -> 10 U71_0(30,29) -> 10 U71_0(30,30) -> 10 U71_1(14,14) -> 40 U71_1(14,16) -> 40 U71_1(14,17) -> 40 U71_1(14,23) -> 40 U71_1(14,24) -> 40 U71_1(14,25) -> 40 U71_1(14,26) -> 40 U71_1(14,29) -> 40 U71_1(14,30) -> 40 U71_1(16,14) -> 40 U71_1(16,16) -> 40 U71_1(16,17) -> 40 U71_1(16,23) -> 40 U71_1(16,24) -> 40 U71_1(16,25) -> 40 U71_1(16,26) -> 40 U71_1(16,29) -> 40 U71_1(16,30) -> 40 U71_1(17,14) -> 40 U71_1(17,16) -> 40 U71_1(17,17) -> 40 U71_1(17,23) -> 40 U71_1(17,24) -> 40 U71_1(17,25) -> 40 U71_1(17,26) -> 40 U71_1(17,29) -> 40 U71_1(17,30) -> 40 U71_1(23,14) -> 40 U71_1(23,16) -> 40 U71_1(23,17) -> 40 U71_1(23,23) -> 40 U71_1(23,24) -> 40 U71_1(23,25) -> 40 U71_1(23,26) -> 40 U71_1(23,29) -> 40 U71_1(23,30) -> 40 U71_1(24,14) -> 40 U71_1(24,16) -> 40 U71_1(24,17) -> 40 U71_1(24,23) -> 40 U71_1(24,24) -> 40 U71_1(24,25) -> 40 U71_1(24,26) -> 40 U71_1(24,29) -> 40 U71_1(24,30) -> 40 U71_1(25,14) -> 40 U71_1(25,16) -> 40 U71_1(25,17) -> 40 U71_1(25,23) -> 40 U71_1(25,24) -> 40 U71_1(25,25) -> 40 U71_1(25,26) -> 40 U71_1(25,29) -> 40 U71_1(25,30) -> 40 U71_1(26,14) -> 40 U71_1(26,16) -> 40 U71_1(26,17) -> 40 U71_1(26,23) -> 40 U71_1(26,24) -> 40 U71_1(26,25) -> 40 U71_1(26,26) -> 40 U71_1(26,29) -> 40 U71_1(26,30) -> 40 U71_1(29,14) -> 40 U71_1(29,16) -> 40 U71_1(29,17) -> 40 U71_1(29,23) -> 40 U71_1(29,24) -> 40 U71_1(29,25) -> 40 U71_1(29,26) -> 40 U71_1(29,29) -> 40 U71_1(29,30) -> 40 U71_1(30,14) -> 40 U71_1(30,16) -> 40 U71_1(30,17) -> 40 U71_1(30,23) -> 40 U71_1(30,24) -> 40 U71_1(30,25) -> 40 U71_1(30,26) -> 40 U71_1(30,29) -> 40 U71_1(30,30) -> 40 U72_0(14) -> 11 U72_0(16) -> 11 U72_0(17) -> 11 U72_0(23) -> 11 U72_0(24) -> 11 U72_0(25) -> 11 U72_0(26) -> 11 U72_0(29) -> 11 U72_0(30) -> 11 U72_1(14) -> 41 U72_1(16) -> 41 U72_1(17) -> 41 U72_1(23) -> 41 U72_1(24) -> 41 U72_1(25) -> 41 U72_1(26) -> 41 U72_1(29) -> 41 U72_1(30) -> 41 U81_0(14) -> 12 U81_0(16) -> 12 U81_0(17) -> 12 U81_0(23) -> 12 U81_0(24) -> 12 U81_0(25) -> 12 U81_0(26) -> 12 U81_0(29) -> 12 U81_0(30) -> 12 U81_1(14) -> 42 U81_1(16) -> 42 U81_1(17) -> 42 U81_1(23) -> 42 U81_1(24) -> 42 U81_1(25) -> 42 U81_1(26) -> 42 U81_1(29) -> 42 U81_1(30) -> 42 ___0(14,14) -> 13 ___0(14,16) -> 13 ___0(14,17) -> 13 ___0(14,23) -> 13 ___0(14,24) -> 13 ___0(14,25) -> 13 ___0(14,26) -> 13 ___0(14,29) -> 13 ___0(14,30) -> 13 ___0(16,14) -> 13 ___0(16,16) -> 13 ___0(16,17) -> 13 ___0(16,23) -> 13 ___0(16,24) -> 13 ___0(16,25) -> 13 ___0(16,26) -> 13 ___0(16,29) -> 13 ___0(16,30) -> 13 ___0(17,14) -> 13 ___0(17,16) -> 13 ___0(17,17) -> 13 ___0(17,23) -> 13 ___0(17,24) -> 13 ___0(17,25) -> 13 ___0(17,26) -> 13 ___0(17,29) -> 13 ___0(17,30) -> 13 ___0(23,14) -> 13 ___0(23,16) -> 13 ___0(23,17) -> 13 ___0(23,23) -> 13 ___0(23,24) -> 13 ___0(23,25) -> 13 ___0(23,26) -> 13 ___0(23,29) -> 13 ___0(23,30) -> 13 ___0(24,14) -> 13 ___0(24,16) -> 13 ___0(24,17) -> 13 ___0(24,23) -> 13 ___0(24,24) -> 13 ___0(24,25) -> 13 ___0(24,26) -> 13 ___0(24,29) -> 13 ___0(24,30) -> 13 ___0(25,14) -> 13 ___0(25,16) -> 13 ___0(25,17) -> 13 ___0(25,23) -> 13 ___0(25,24) -> 13 ___0(25,25) -> 13 ___0(25,26) -> 13 ___0(25,29) -> 13 ___0(25,30) -> 13 ___0(26,14) -> 13 ___0(26,16) -> 13 ___0(26,17) -> 13 ___0(26,23) -> 13 ___0(26,24) -> 13 ___0(26,25) -> 13 ___0(26,26) -> 13 ___0(26,29) -> 13 ___0(26,30) -> 13 ___0(29,14) -> 13 ___0(29,16) -> 13 ___0(29,17) -> 13 ___0(29,23) -> 13 ___0(29,24) -> 13 ___0(29,25) -> 13 ___0(29,26) -> 13 ___0(29,29) -> 13 ___0(29,30) -> 13 ___0(30,14) -> 13 ___0(30,16) -> 13 ___0(30,17) -> 13 ___0(30,23) -> 13 ___0(30,24) -> 13 ___0(30,25) -> 13 ___0(30,26) -> 13 ___0(30,29) -> 13 ___0(30,30) -> 13 ___1(14,14) -> 43 ___1(14,16) -> 43 ___1(14,17) -> 43 ___1(14,23) -> 43 ___1(14,24) -> 43 ___1(14,25) -> 43 ___1(14,26) -> 43 ___1(14,29) -> 43 ___1(14,30) -> 43 ___1(16,14) -> 43 ___1(16,16) -> 43 ___1(16,17) -> 43 ___1(16,23) -> 43 ___1(16,24) -> 43 ___1(16,25) -> 43 ___1(16,26) -> 43 ___1(16,29) -> 43 ___1(16,30) -> 43 ___1(17,14) -> 43 ___1(17,16) -> 43 ___1(17,17) -> 43 ___1(17,23) -> 43 ___1(17,24) -> 43 ___1(17,25) -> 43 ___1(17,26) -> 43 ___1(17,29) -> 43 ___1(17,30) -> 43 ___1(23,14) -> 43 ___1(23,16) -> 43 ___1(23,17) -> 43 ___1(23,23) -> 43 ___1(23,24) -> 43 ___1(23,25) -> 43 ___1(23,26) -> 43 ___1(23,29) -> 43 ___1(23,30) -> 43 ___1(24,14) -> 43 ___1(24,16) -> 43 ___1(24,17) -> 43 ___1(24,23) -> 43 ___1(24,24) -> 43 ___1(24,25) -> 43 ___1(24,26) -> 43 ___1(24,29) -> 43 ___1(24,30) -> 43 ___1(25,14) -> 43 ___1(25,16) -> 43 ___1(25,17) -> 43 ___1(25,23) -> 43 ___1(25,24) -> 43 ___1(25,25) -> 43 ___1(25,26) -> 43 ___1(25,29) -> 43 ___1(25,30) -> 43 ___1(26,14) -> 43 ___1(26,16) -> 43 ___1(26,17) -> 43 ___1(26,23) -> 43 ___1(26,24) -> 43 ___1(26,25) -> 43 ___1(26,26) -> 43 ___1(26,29) -> 43 ___1(26,30) -> 43 ___1(29,14) -> 43 ___1(29,16) -> 43 ___1(29,17) -> 43 ___1(29,23) -> 43 ___1(29,24) -> 43 ___1(29,25) -> 43 ___1(29,26) -> 43 ___1(29,29) -> 43 ___1(29,30) -> 43 ___1(30,14) -> 43 ___1(30,16) -> 43 ___1(30,17) -> 43 ___1(30,23) -> 43 ___1(30,24) -> 43 ___1(30,25) -> 43 ___1(30,26) -> 43 ___1(30,29) -> 43 ___1(30,30) -> 43 a_0() -> 14 a_1() -> 49 active_0(14) -> 15 active_0(16) -> 15 active_0(17) -> 15 active_0(23) -> 15 active_0(24) -> 15 active_0(25) -> 15 active_0(26) -> 15 active_0(29) -> 15 active_0(30) -> 15 active_1(14) -> 50 active_1(16) -> 50 active_1(17) -> 50 active_1(23) -> 50 active_1(24) -> 50 active_1(25) -> 50 active_1(26) -> 50 active_1(29) -> 50 active_1(30) -> 50 active_2(49) -> 51 e_0() -> 16 e_1() -> 49 i_0() -> 17 i_1() -> 49 isList_0(14) -> 18 isList_0(16) -> 18 isList_0(17) -> 18 isList_0(23) -> 18 isList_0(24) -> 18 isList_0(25) -> 18 isList_0(26) -> 18 isList_0(29) -> 18 isList_0(30) -> 18 isList_1(14) -> 44 isList_1(16) -> 44 isList_1(17) -> 44 isList_1(23) -> 44 isList_1(24) -> 44 isList_1(25) -> 44 isList_1(26) -> 44 isList_1(29) -> 44 isList_1(30) -> 44 isNeList_0(14) -> 19 isNeList_0(16) -> 19 isNeList_0(17) -> 19 isNeList_0(23) -> 19 isNeList_0(24) -> 19 isNeList_0(25) -> 19 isNeList_0(26) -> 19 isNeList_0(29) -> 19 isNeList_0(30) -> 19 isNeList_1(14) -> 45 isNeList_1(16) -> 45 isNeList_1(17) -> 45 isNeList_1(23) -> 45 isNeList_1(24) -> 45 isNeList_1(25) -> 45 isNeList_1(26) -> 45 isNeList_1(29) -> 45 isNeList_1(30) -> 45 isNePal_0(14) -> 20 isNePal_0(16) -> 20 isNePal_0(17) -> 20 isNePal_0(23) -> 20 isNePal_0(24) -> 20 isNePal_0(25) -> 20 isNePal_0(26) -> 20 isNePal_0(29) -> 20 isNePal_0(30) -> 20 isNePal_1(14) -> 46 isNePal_1(16) -> 46 isNePal_1(17) -> 46 isNePal_1(23) -> 46 isNePal_1(24) -> 46 isNePal_1(25) -> 46 isNePal_1(26) -> 46 isNePal_1(29) -> 46 isNePal_1(30) -> 46 isPal_0(14) -> 21 isPal_0(16) -> 21 isPal_0(17) -> 21 isPal_0(23) -> 21 isPal_0(24) -> 21 isPal_0(25) -> 21 isPal_0(26) -> 21 isPal_0(29) -> 21 isPal_0(30) -> 21 isPal_1(14) -> 47 isPal_1(16) -> 47 isPal_1(17) -> 47 isPal_1(23) -> 47 isPal_1(24) -> 47 isPal_1(25) -> 47 isPal_1(26) -> 47 isPal_1(29) -> 47 isPal_1(30) -> 47 isQid_0(14) -> 22 isQid_0(16) -> 22 isQid_0(17) -> 22 isQid_0(23) -> 22 isQid_0(24) -> 22 isQid_0(25) -> 22 isQid_0(26) -> 22 isQid_0(29) -> 22 isQid_0(30) -> 22 isQid_1(14) -> 48 isQid_1(16) -> 48 isQid_1(17) -> 48 isQid_1(23) -> 48 isQid_1(24) -> 48 isQid_1(25) -> 48 isQid_1(26) -> 48 isQid_1(29) -> 48 isQid_1(30) -> 48 mark_0(14) -> 23 mark_0(16) -> 23 mark_0(17) -> 23 mark_0(23) -> 23 mark_0(24) -> 23 mark_0(25) -> 23 mark_0(26) -> 23 mark_0(29) -> 23 mark_0(30) -> 23 mark_1(31) -> 1 mark_1(31) -> 31 mark_1(32) -> 2 mark_1(32) -> 32 mark_1(33) -> 3 mark_1(33) -> 33 mark_1(34) -> 4 mark_1(34) -> 34 mark_1(35) -> 5 mark_1(35) -> 35 mark_1(36) -> 6 mark_1(36) -> 36 mark_1(37) -> 7 mark_1(37) -> 37 mark_1(38) -> 8 mark_1(38) -> 38 mark_1(39) -> 9 mark_1(39) -> 39 mark_1(40) -> 10 mark_1(40) -> 40 mark_1(41) -> 11 mark_1(41) -> 41 mark_1(42) -> 12 mark_1(42) -> 42 mark_1(43) -> 13 mark_1(43) -> 43 nil_0() -> 24 nil_1() -> 49 o_0() -> 25 o_1() -> 49 ok_0(14) -> 26 ok_0(16) -> 26 ok_0(17) -> 26 ok_0(23) -> 26 ok_0(24) -> 26 ok_0(25) -> 26 ok_0(26) -> 26 ok_0(29) -> 26 ok_0(30) -> 26 ok_1(31) -> 1 ok_1(31) -> 31 ok_1(32) -> 2 ok_1(32) -> 32 ok_1(33) -> 3 ok_1(33) -> 33 ok_1(34) -> 4 ok_1(34) -> 34 ok_1(35) -> 5 ok_1(35) -> 35 ok_1(36) -> 6 ok_1(36) -> 36 ok_1(37) -> 7 ok_1(37) -> 37 ok_1(38) -> 8 ok_1(38) -> 38 ok_1(39) -> 9 ok_1(39) -> 39 ok_1(40) -> 10 ok_1(40) -> 40 ok_1(41) -> 11 ok_1(41) -> 41 ok_1(42) -> 12 ok_1(42) -> 42 ok_1(43) -> 13 ok_1(43) -> 43 ok_1(44) -> 18 ok_1(44) -> 44 ok_1(45) -> 19 ok_1(45) -> 45 ok_1(46) -> 20 ok_1(46) -> 46 ok_1(47) -> 21 ok_1(47) -> 47 ok_1(48) -> 22 ok_1(48) -> 48 ok_1(49) -> 27 ok_1(49) -> 50 proper_0(14) -> 27 proper_0(16) -> 27 proper_0(17) -> 27 proper_0(23) -> 27 proper_0(24) -> 27 proper_0(25) -> 27 proper_0(26) -> 27 proper_0(29) -> 27 proper_0(30) -> 27 proper_1(14) -> 50 proper_1(16) -> 50 proper_1(17) -> 50 proper_1(23) -> 50 proper_1(24) -> 50 proper_1(25) -> 50 proper_1(26) -> 50 proper_1(29) -> 50 proper_1(30) -> 50 top_0(14) -> 28 top_0(16) -> 28 top_0(17) -> 28 top_0(23) -> 28 top_0(24) -> 28 top_0(25) -> 28 top_0(26) -> 28 top_0(29) -> 28 top_0(30) -> 28 top_1(50) -> 28 top_2(51) -> 28 tt_0() -> 29 tt_1() -> 49 u_0() -> 30 u_1() -> 49 ** 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)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(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(tt()) active(U21(X1,X2)) -> U21(active(X1),X2) active(U21(tt(),V2)) -> mark(U22(isList(V2))) active(U22(X)) -> U22(active(X)) active(U22(tt())) -> mark(tt()) active(U31(X)) -> U31(active(X)) active(U31(tt())) -> mark(tt()) active(U41(X1,X2)) -> U41(active(X1),X2) active(U41(tt(),V2)) -> mark(U42(isNeList(V2))) active(U42(X)) -> U42(active(X)) active(U42(tt())) -> mark(tt()) active(U51(X1,X2)) -> U51(active(X1),X2) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U52(X)) -> U52(active(X)) active(U52(tt())) -> mark(tt()) active(U61(X)) -> U61(active(X)) active(U61(tt())) -> mark(tt()) active(U71(X1,X2)) -> U71(active(X1),X2) active(U71(tt(),P)) -> mark(U72(isPal(P))) active(U72(X)) -> U72(active(X)) active(U72(tt())) -> mark(tt()) active(U81(X)) -> U81(active(X)) active(U81(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(isList(V)) -> mark(U11(isNeList(V))) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isList(nil())) -> mark(tt()) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isPal(V)) -> mark(U81(isNePal(V))) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) isQid(ok(X)) -> ok(isQid(X)) proper(U11(X)) -> U11(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(nil()) -> ok(nil()) proper(o()) -> ok(o()) proper(tt()) -> ok(tt()) proper(u()) -> ok(u()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {U11/1,U21/2,U22/1,U31/1,U41/2,U42/1,U51/2,U52/1,U61/1,U71/2,U72/1,U81/1,__/2,active/1,isList/1,isNeList/1 ,isNePal/1,isPal/1,isQid/1,proper/1,top/1} / {a/0,e/0,i/0,mark/1,nil/0,o/0,ok/1,tt/0,u/0} - Obligation: runtime complexity wrt. defined symbols {U11,U21,U22,U31,U41,U42,U51,U52,U61,U71,U72,U81,__,active,isList ,isNeList,isNePal,isPal,isQid,proper,top} and constructors {a,e,i,mark,nil,o,ok,tt,u} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))