/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),?) * Step 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)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U15(mark(X1),X2) -> mark(U15(X1,X2)) U15(ok(X1),ok(X2)) -> ok(U15(X1,X2)) U16(mark(X)) -> mark(U16(X)) U16(ok(X)) -> ok(U16(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U23(ok(X)) -> ok(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U32(ok(X)) -> ok(U32(X)) U41(mark(X)) -> mark(U41(X)) U41(ok(X)) -> ok(U41(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3)) U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3)) U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3)) U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3)) U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3)) U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3)) U64(mark(X1),X2,X3) -> mark(U64(X1,X2,X3)) U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(X1,X2,X3)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(X1,X2)) -> U15(active(X1),X2) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(X)) -> U16(active(X)) active(U16(tt())) -> mark(tt()) active(U21(X1,X2)) -> U21(active(X1),X2) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(X1,X2)) -> U22(active(X1),X2) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(X)) -> U23(active(X)) active(U23(tt())) -> mark(tt()) active(U31(X1,X2)) -> U31(active(X1),X2) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(X)) -> U32(active(X)) active(U32(tt())) -> mark(tt()) active(U41(X)) -> U41(active(X)) active(U41(tt())) -> mark(tt()) active(U51(X1,X2)) -> U51(active(X1),X2) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(X1,X2)) -> U52(active(X1),X2) active(U52(tt(),N)) -> mark(N) active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(X1,X2,X3)) -> U64(active(X1),X2,X3) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) active(plus(X1,X2)) -> plus(X1,active(X2)) active(plus(X1,X2)) -> plus(active(X1),X2) active(s(X)) -> s(active(X)) isNat(ok(X)) -> ok(isNat(X)) isNatKind(ok(X)) -> ok(isNatKind(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(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U15(X1,X2)) -> U15(proper(X1),proper(X2)) proper(U16(X)) -> U16(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(U41(X)) -> U41(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3)) proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3)) proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3)) proper(U64(X1,X2,X3)) -> U64(proper(X1),proper(X2),proper(X3)) proper(isNat(X)) -> isNat(proper(X)) proper(isNatKind(X)) -> isNatKind(proper(X)) 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,U13/3,U14/3,U15/2,U16/1,U21/2,U22/2,U23/1,U31/2,U32/1,U41/1,U51/2,U52/2,U61/3,U62/3,U63/3,U64/3 ,active/1,isNat/1,isNatKind/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,U13,U14,U15,U16,U21,U22,U23,U31,U32,U41,U51,U52,U61,U62 ,U63,U64,active,isNat,isNatKind,plus,proper,s,top} and constructors {0,mark,ok,tt} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: 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)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U15(mark(X1),X2) -> mark(U15(X1,X2)) U15(ok(X1),ok(X2)) -> ok(U15(X1,X2)) U16(mark(X)) -> mark(U16(X)) U16(ok(X)) -> ok(U16(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U23(ok(X)) -> ok(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U32(ok(X)) -> ok(U32(X)) U41(mark(X)) -> mark(U41(X)) U41(ok(X)) -> ok(U41(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3)) U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3)) U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3)) U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3)) U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3)) U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3)) U64(mark(X1),X2,X3) -> mark(U64(X1,X2,X3)) U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(X1,X2,X3)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(X1,X2)) -> U15(active(X1),X2) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(X)) -> U16(active(X)) active(U16(tt())) -> mark(tt()) active(U21(X1,X2)) -> U21(active(X1),X2) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(X1,X2)) -> U22(active(X1),X2) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(X)) -> U23(active(X)) active(U23(tt())) -> mark(tt()) active(U31(X1,X2)) -> U31(active(X1),X2) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(X)) -> U32(active(X)) active(U32(tt())) -> mark(tt()) active(U41(X)) -> U41(active(X)) active(U41(tt())) -> mark(tt()) active(U51(X1,X2)) -> U51(active(X1),X2) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(X1,X2)) -> U52(active(X1),X2) active(U52(tt(),N)) -> mark(N) active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(X1,X2,X3)) -> U64(active(X1),X2,X3) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) active(plus(X1,X2)) -> plus(X1,active(X2)) active(plus(X1,X2)) -> plus(active(X1),X2) active(s(X)) -> s(active(X)) isNat(ok(X)) -> ok(isNat(X)) isNatKind(ok(X)) -> ok(isNatKind(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(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U15(X1,X2)) -> U15(proper(X1),proper(X2)) proper(U16(X)) -> U16(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(U41(X)) -> U41(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3)) proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3)) proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3)) proper(U64(X1,X2,X3)) -> U64(proper(X1),proper(X2),proper(X3)) proper(isNat(X)) -> isNat(proper(X)) proper(isNatKind(X)) -> isNatKind(proper(X)) 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,U13/3,U14/3,U15/2,U16/1,U21/2,U22/2,U23/1,U31/2,U32/1,U41/1,U51/2,U52/2,U61/3,U62/3,U63/3,U64/3 ,active/1,isNat/1,isNatKind/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,U13,U14,U15,U16,U21,U22,U23,U31,U32,U41,U51,U52,U61,U62 ,U63,U64,active,isNat,isNatKind,plus,proper,s,top} and constructors {0,mark,ok,tt} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 3: 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)) U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3)) U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3)) U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3)) U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3)) U15(mark(X1),X2) -> mark(U15(X1,X2)) U15(ok(X1),ok(X2)) -> ok(U15(X1,X2)) U16(mark(X)) -> mark(U16(X)) U16(ok(X)) -> ok(U16(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(mark(X1),X2) -> mark(U22(X1,X2)) U22(ok(X1),ok(X2)) -> ok(U22(X1,X2)) U23(mark(X)) -> mark(U23(X)) U23(ok(X)) -> ok(U23(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U32(mark(X)) -> mark(U32(X)) U32(ok(X)) -> ok(U32(X)) U41(mark(X)) -> mark(U41(X)) U41(ok(X)) -> ok(U41(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(mark(X1),X2) -> mark(U52(X1,X2)) U52(ok(X1),ok(X2)) -> ok(U52(X1,X2)) U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3)) U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3)) U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3)) U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3)) U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3)) U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3)) U64(mark(X1),X2,X3) -> mark(U64(X1,X2,X3)) U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(X1,X2,X3)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(X1,X2)) -> U15(active(X1),X2) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(X)) -> U16(active(X)) active(U16(tt())) -> mark(tt()) active(U21(X1,X2)) -> U21(active(X1),X2) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(X1,X2)) -> U22(active(X1),X2) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(X)) -> U23(active(X)) active(U23(tt())) -> mark(tt()) active(U31(X1,X2)) -> U31(active(X1),X2) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(X)) -> U32(active(X)) active(U32(tt())) -> mark(tt()) active(U41(X)) -> U41(active(X)) active(U41(tt())) -> mark(tt()) active(U51(X1,X2)) -> U51(active(X1),X2) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(X1,X2)) -> U52(active(X1),X2) active(U52(tt(),N)) -> mark(N) active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(X1,X2,X3)) -> U64(active(X1),X2,X3) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) active(plus(X1,X2)) -> plus(X1,active(X2)) active(plus(X1,X2)) -> plus(active(X1),X2) active(s(X)) -> s(active(X)) isNat(ok(X)) -> ok(isNat(X)) isNatKind(ok(X)) -> ok(isNatKind(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(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3)) proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3)) proper(U15(X1,X2)) -> U15(proper(X1),proper(X2)) proper(U16(X)) -> U16(proper(X)) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X1,X2)) -> U22(proper(X1),proper(X2)) proper(U23(X)) -> U23(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U32(X)) -> U32(proper(X)) proper(U41(X)) -> U41(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X1,X2)) -> U52(proper(X1),proper(X2)) proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3)) proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3)) proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3)) proper(U64(X1,X2,X3)) -> U64(proper(X1),proper(X2),proper(X3)) proper(isNat(X)) -> isNat(proper(X)) proper(isNatKind(X)) -> isNatKind(proper(X)) 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,U13/3,U14/3,U15/2,U16/1,U21/2,U22/2,U23/1,U31/2,U32/1,U41/1,U51/2,U52/2,U61/3,U62/3,U63/3,U64/3 ,active/1,isNat/1,isNatKind/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,U13,U14,U15,U16,U21,U22,U23,U31,U32,U41,U51,U52,U61,U62 ,U63,U64,active,isNat,isNatKind,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){}] WORST_CASE(Omega(n^1),?)