Runti Compl Full Rewri 10127 pair #381902957

details

property	value
status	complete
benchmark	PEANO_complete-noand_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n069.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rc
runtime (wallclock)	295.174050093 seconds
cpu usage	771.256750848
max memory	2.3210348544E10

stage attributes

key	value
output-size	5459
starexec-result	WORST_CASE(Omega(n^1),?)

output

/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^1),?)
* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            U11(tt(),V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2))
            U12(tt(),V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2))
            U13(tt(),V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2))
            U14(tt(),V1,V2) -> U15(isNat(activate(V1)),activate(V2))
            U15(tt(),V2) -> U16(isNat(activate(V2)))
            U16(tt()) -> tt()
            U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1))
            U22(tt(),V1) -> U23(isNat(activate(V1)))
            U23(tt()) -> tt()
            U31(tt(),V2) -> U32(isNatKind(activate(V2)))
            U32(tt()) -> tt()
            U41(tt()) -> tt()
            U51(tt(),N) -> U52(isNatKind(activate(N)),activate(N))
            U52(tt(),N) -> activate(N)
            U61(tt(),M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N))
            U62(tt(),M,N) -> U63(isNat(activate(N)),activate(M),activate(N))
            U63(tt(),M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N))
            U64(tt(),M,N) -> s(plus(activate(N),activate(M)))
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__plus(X1,X2)) -> plus(X1,X2)
            activate(n__s(X)) -> s(X)
            isNat(n__0()) -> tt()
            isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2))
            isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
            isNatKind(n__0()) -> tt()
            isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2))
            isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1)))
            plus(N,0()) -> U51(isNat(N),N)
            plus(N,s(M)) -> U61(isNat(M),M,N)
            plus(X1,X2) -> n__plus(X1,X2)
            s(X) -> n__s(X)
        - Signature:
            {0/0,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,activate/1,isNat/1,isNatKind/1,plus/2,s/1} / {n__0/0,n__plus/2,n__s/1,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,U11,U12,U13,U14,U15,U16,U21,U22,U23,U31,U32,U41,U51,U52,U61,U62
            ,U63,U64,activate,isNat,isNatKind,plus,s} and constructors {n__0,n__plus,n__s,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            U11(tt(),V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2))
            U12(tt(),V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2))
            U13(tt(),V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2))
            U14(tt(),V1,V2) -> U15(isNat(activate(V1)),activate(V2))
            U15(tt(),V2) -> U16(isNat(activate(V2)))
            U16(tt()) -> tt()
            U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1))
            U22(tt(),V1) -> U23(isNat(activate(V1)))
            U23(tt()) -> tt()
            U31(tt(),V2) -> U32(isNatKind(activate(V2)))
            U32(tt()) -> tt()
            U41(tt()) -> tt()
            U51(tt(),N) -> U52(isNatKind(activate(N)),activate(N))
            U52(tt(),N) -> activate(N)
            U61(tt(),M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N))
            U62(tt(),M,N) -> U63(isNat(activate(N)),activate(M),activate(N))
            U63(tt(),M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N))
            U64(tt(),M,N) -> s(plus(activate(N),activate(M)))
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__plus(X1,X2)) -> plus(X1,X2)
            activate(n__s(X)) -> s(X)
            isNat(n__0()) -> tt()
            isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2))
            isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
            isNatKind(n__0()) -> tt()
            isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2))
            isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1)))
            plus(N,0()) -> U51(isNat(N),N)
            plus(N,s(M)) -> U61(isNat(M),M,N)
            plus(X1,X2) -> n__plus(X1,X2)
            s(X) -> n__s(X)
        - Signature:
            {0/0,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,activate/1,isNat/1,isNatKind/1,plus/2,s/1} / {n__0/0,n__plus/2,n__s/1,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,U11,U12,U13,U14,U15,U16,U21,U22,U23,U31,U32,U41,U51,U52,U61,U62
            ,U63,U64,activate,isNat,isNatKind,plus,s} and constructors {n__0,n__plus,n__s,tt}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          isNatKind(x){x -> n__plus(x,u)} =

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