/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: a__U11(X1,X2) -> U11(X1,X2) a__U11(tt(),V2) -> a__U12(a__isNat(V2)) a__U12(X) -> U12(X) a__U12(tt()) -> tt() a__U21(X) -> U21(X) a__U21(tt()) -> tt() a__U31(X1,X2) -> U31(X1,X2) a__U31(tt(),V2) -> a__U32(a__isNat(V2)) a__U32(X) -> U32(X) a__U32(tt()) -> tt() a__U41(X1,X2) -> U41(X1,X2) a__U41(tt(),N) -> mark(N) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U51(tt(),M,N) -> a__U52(a__isNat(N),M,N) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U52(tt(),M,N) -> s(a__plus(mark(N),mark(M))) a__U61(X) -> U61(X) a__U61(tt()) -> 0() a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U71(tt(),M,N) -> a__U72(a__isNat(N),M,N) a__U72(X1,X2,X3) -> U72(X1,X2,X3) a__U72(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) a__isNat(X) -> isNat(X) a__isNat(0()) -> tt() a__isNat(plus(V1,V2)) -> a__U11(a__isNat(V1),V2) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__isNat(x(V1,V2)) -> a__U31(a__isNat(V1),V2) a__plus(N,0()) -> a__U41(a__isNat(N),N) a__plus(N,s(M)) -> a__U51(a__isNat(M),M,N) a__plus(X1,X2) -> plus(X1,X2) a__x(N,0()) -> a__U61(a__isNat(N)) a__x(N,s(M)) -> a__U71(a__isNat(M),M,N) a__x(X1,X2) -> x(X1,X2) mark(0()) -> 0() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2)) -> a__U41(mark(X1),X2) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2,X3)) -> a__U72(mark(X1),X2,X3) mark(isNat(X)) -> a__isNat(X) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(s(X)) -> s(mark(X)) mark(tt()) -> tt() mark(x(X1,X2)) -> a__x(mark(X1),mark(X2)) - Signature: {a__U11/2,a__U12/1,a__U21/1,a__U31/2,a__U32/1,a__U41/2,a__U51/3,a__U52/3,a__U61/1,a__U71/3,a__U72/3 ,a__isNat/1,a__plus/2,a__x/2,mark/1} / {0/0,U11/2,U12/1,U21/1,U31/2,U32/1,U41/2,U51/3,U52/3,U61/1,U71/3 ,U72/3,isNat/1,plus/2,s/1,tt/0,x/2} - Obligation: runtime complexity wrt. defined symbols {a__U11,a__U12,a__U21,a__U31,a__U32,a__U41,a__U51,a__U52,a__U61 ,a__U71,a__U72,a__isNat,a__plus,a__x,mark} and constructors {0,U11,U12,U21,U31,U32,U41,U51,U52,U61,U71,U72 ,isNat,plus,s,tt,x} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__U11(X1,X2) -> U11(X1,X2) a__U11(tt(),V2) -> a__U12(a__isNat(V2)) a__U12(X) -> U12(X) a__U12(tt()) -> tt() a__U21(X) -> U21(X) a__U21(tt()) -> tt() a__U31(X1,X2) -> U31(X1,X2) a__U31(tt(),V2) -> a__U32(a__isNat(V2)) a__U32(X) -> U32(X) a__U32(tt()) -> tt() a__U41(X1,X2) -> U41(X1,X2) a__U41(tt(),N) -> mark(N) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U51(tt(),M,N) -> a__U52(a__isNat(N),M,N) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U52(tt(),M,N) -> s(a__plus(mark(N),mark(M))) a__U61(X) -> U61(X) a__U61(tt()) -> 0() a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U71(tt(),M,N) -> a__U72(a__isNat(N),M,N) a__U72(X1,X2,X3) -> U72(X1,X2,X3) a__U72(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) a__isNat(X) -> isNat(X) a__isNat(0()) -> tt() a__isNat(plus(V1,V2)) -> a__U11(a__isNat(V1),V2) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__isNat(x(V1,V2)) -> a__U31(a__isNat(V1),V2) a__plus(N,0()) -> a__U41(a__isNat(N),N) a__plus(N,s(M)) -> a__U51(a__isNat(M),M,N) a__plus(X1,X2) -> plus(X1,X2) a__x(N,0()) -> a__U61(a__isNat(N)) a__x(N,s(M)) -> a__U71(a__isNat(M),M,N) a__x(X1,X2) -> x(X1,X2) mark(0()) -> 0() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2)) -> a__U41(mark(X1),X2) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2,X3)) -> a__U72(mark(X1),X2,X3) mark(isNat(X)) -> a__isNat(X) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(s(X)) -> s(mark(X)) mark(tt()) -> tt() mark(x(X1,X2)) -> a__x(mark(X1),mark(X2)) - Signature: {a__U11/2,a__U12/1,a__U21/1,a__U31/2,a__U32/1,a__U41/2,a__U51/3,a__U52/3,a__U61/1,a__U71/3,a__U72/3 ,a__isNat/1,a__plus/2,a__x/2,mark/1} / {0/0,U11/2,U12/1,U21/1,U31/2,U32/1,U41/2,U51/3,U52/3,U61/1,U71/3 ,U72/3,isNat/1,plus/2,s/1,tt/0,x/2} - Obligation: runtime complexity wrt. defined symbols {a__U11,a__U12,a__U21,a__U31,a__U32,a__U41,a__U51,a__U52,a__U61 ,a__U71,a__U72,a__isNat,a__plus,a__x,mark} and constructors {0,U11,U12,U21,U31,U32,U41,U51,U52,U61,U71,U72 ,isNat,plus,s,tt,x} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 3: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__U11(X1,X2) -> U11(X1,X2) a__U11(tt(),V2) -> a__U12(a__isNat(V2)) a__U12(X) -> U12(X) a__U12(tt()) -> tt() a__U21(X) -> U21(X) a__U21(tt()) -> tt() a__U31(X1,X2) -> U31(X1,X2) a__U31(tt(),V2) -> a__U32(a__isNat(V2)) a__U32(X) -> U32(X) a__U32(tt()) -> tt() a__U41(X1,X2) -> U41(X1,X2) a__U41(tt(),N) -> mark(N) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U51(tt(),M,N) -> a__U52(a__isNat(N),M,N) a__U52(X1,X2,X3) -> U52(X1,X2,X3) a__U52(tt(),M,N) -> s(a__plus(mark(N),mark(M))) a__U61(X) -> U61(X) a__U61(tt()) -> 0() a__U71(X1,X2,X3) -> U71(X1,X2,X3) a__U71(tt(),M,N) -> a__U72(a__isNat(N),M,N) a__U72(X1,X2,X3) -> U72(X1,X2,X3) a__U72(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) a__isNat(X) -> isNat(X) a__isNat(0()) -> tt() a__isNat(plus(V1,V2)) -> a__U11(a__isNat(V1),V2) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__isNat(x(V1,V2)) -> a__U31(a__isNat(V1),V2) a__plus(N,0()) -> a__U41(a__isNat(N),N) a__plus(N,s(M)) -> a__U51(a__isNat(M),M,N) a__plus(X1,X2) -> plus(X1,X2) a__x(N,0()) -> a__U61(a__isNat(N)) a__x(N,s(M)) -> a__U71(a__isNat(M),M,N) a__x(X1,X2) -> x(X1,X2) mark(0()) -> 0() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2)) -> a__U41(mark(X1),X2) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3) mark(U72(X1,X2,X3)) -> a__U72(mark(X1),X2,X3) mark(isNat(X)) -> a__isNat(X) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(s(X)) -> s(mark(X)) mark(tt()) -> tt() mark(x(X1,X2)) -> a__x(mark(X1),mark(X2)) - Signature: {a__U11/2,a__U12/1,a__U21/1,a__U31/2,a__U32/1,a__U41/2,a__U51/3,a__U52/3,a__U61/1,a__U71/3,a__U72/3 ,a__isNat/1,a__plus/2,a__x/2,mark/1} / {0/0,U11/2,U12/1,U21/1,U31/2,U32/1,U41/2,U51/3,U52/3,U61/1,U71/3 ,U72/3,isNat/1,plus/2,s/1,tt/0,x/2} - Obligation: runtime complexity wrt. defined symbols {a__U11,a__U12,a__U21,a__U31,a__U32,a__U41,a__U51,a__U52,a__U61 ,a__U71,a__U72,a__isNat,a__plus,a__x,mark} and constructors {0,U11,U12,U21,U31,U32,U41,U51,U52,U61,U71,U72 ,isNat,plus,s,tt,x} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: a__isNat(x){x -> plus(x,y)} = a__isNat(plus(x,y)) ->^+ a__U11(a__isNat(x),y) = C[a__isNat(x) = a__isNat(x){}] WORST_CASE(Omega(n^1),?)