Problem Transformed CSR 04 MYNAT complete noand GM

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 MYNAT complete noand GM

stdout:

MAYBE

Problem:
a__U101(tt(),M,N) -> a__U102(a__isNatKind(M),M,N)
a__U102(tt(),M,N) -> a__U103(a__isNat(N),M,N)
a__U103(tt(),M,N) -> a__U104(a__isNatKind(N),M,N)
a__U104(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N))
a__U11(tt(),V1,V2) -> a__U12(a__isNatKind(V1),V1,V2)
a__U12(tt(),V1,V2) -> a__U13(a__isNatKind(V2),V1,V2)
a__U13(tt(),V1,V2) -> a__U14(a__isNatKind(V2),V1,V2)
a__U14(tt(),V1,V2) -> a__U15(a__isNat(V1),V2)
a__U15(tt(),V2) -> a__U16(a__isNat(V2))
a__U16(tt()) -> tt()
a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1)
a__U22(tt(),V1) -> a__U23(a__isNat(V1))
a__U23(tt()) -> tt()
a__U31(tt(),V1,V2) -> a__U32(a__isNatKind(V1),V1,V2)
a__U32(tt(),V1,V2) -> a__U33(a__isNatKind(V2),V1,V2)
a__U33(tt(),V1,V2) -> a__U34(a__isNatKind(V2),V1,V2)
a__U34(tt(),V1,V2) -> a__U35(a__isNat(V1),V2)
a__U35(tt(),V2) -> a__U36(a__isNat(V2))
a__U36(tt()) -> tt()
a__U41(tt(),V2) -> a__U42(a__isNatKind(V2))
a__U42(tt()) -> tt()
a__U51(tt()) -> tt()
a__U61(tt(),V2) -> a__U62(a__isNatKind(V2))
a__U62(tt()) -> tt()
a__U71(tt(),N) -> a__U72(a__isNatKind(N),N)
a__U72(tt(),N) -> mark(N)
a__U81(tt(),M,N) -> a__U82(a__isNatKind(M),M,N)
a__U82(tt(),M,N) -> a__U83(a__isNat(N),M,N)
a__U83(tt(),M,N) -> a__U84(a__isNatKind(N),M,N)
a__U84(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
a__U91(tt(),N) -> a__U92(a__isNatKind(N))
a__U92(tt()) -> 0()
a__isNat(0()) -> tt()
a__isNat(plus(V1,V2)) -> a__U11(a__isNatKind(V1),V1,V2)
a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1)
a__isNat(x(V1,V2)) -> a__U31(a__isNatKind(V1),V1,V2)
a__isNatKind(0()) -> tt()
a__isNatKind(plus(V1,V2)) -> a__U41(a__isNatKind(V1),V2)
a__isNatKind(s(V1)) -> a__U51(a__isNatKind(V1))
a__isNatKind(x(V1,V2)) -> a__U61(a__isNatKind(V1),V2)
a__plus(N,0()) -> a__U71(a__isNat(N),N)
a__plus(N,s(M)) -> a__U81(a__isNat(M),M,N)
a__x(N,0()) -> a__U91(a__isNat(N),N)
a__x(N,s(M)) -> a__U101(a__isNat(M),M,N)
mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3)
mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3)
mark(isNatKind(X)) -> a__isNatKind(X)
mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3)
mark(isNat(X)) -> a__isNat(X)
mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3)
mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
mark(U13(X1,X2,X3)) -> a__U13(mark(X1),X2,X3)
mark(U14(X1,X2,X3)) -> a__U14(mark(X1),X2,X3)
mark(U15(X1,X2)) -> a__U15(mark(X1),X2)
mark(U16(X)) -> a__U16(mark(X))
mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
mark(U22(X1,X2)) -> a__U22(mark(X1),X2)
mark(U23(X)) -> a__U23(mark(X))
mark(U31(X1,X2,X3)) -> a__U31(mark(X1),X2,X3)
mark(U32(X1,X2,X3)) -> a__U32(mark(X1),X2,X3)
mark(U33(X1,X2,X3)) -> a__U33(mark(X1),X2,X3)
mark(U34(X1,X2,X3)) -> a__U34(mark(X1),X2,X3)
mark(U35(X1,X2)) -> a__U35(mark(X1),X2)
mark(U36(X)) -> a__U36(mark(X))
mark(U41(X1,X2)) -> a__U41(mark(X1),X2)
mark(U42(X)) -> a__U42(mark(X))
mark(U51(X)) -> a__U51(mark(X))
mark(U61(X1,X2)) -> a__U61(mark(X1),X2)
mark(U62(X)) -> a__U62(mark(X))
mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
mark(U72(X1,X2)) -> a__U72(mark(X1),X2)
mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3)
mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3)
mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3)
mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3)
mark(U91(X1,X2)) -> a__U91(mark(X1),X2)
mark(U92(X)) -> a__U92(mark(X))
mark(tt()) -> tt()
mark(s(X)) -> s(mark(X))
mark(0()) -> 0()
a__U101(X1,X2,X3) -> U101(X1,X2,X3)
a__U102(X1,X2,X3) -> U102(X1,X2,X3)
a__isNatKind(X) -> isNatKind(X)
a__U103(X1,X2,X3) -> U103(X1,X2,X3)
a__isNat(X) -> isNat(X)
a__U104(X1,X2,X3) -> U104(X1,X2,X3)
a__plus(X1,X2) -> plus(X1,X2)
a__x(X1,X2) -> x(X1,X2)
a__U11(X1,X2,X3) -> U11(X1,X2,X3)
a__U12(X1,X2,X3) -> U12(X1,X2,X3)
a__U13(X1,X2,X3) -> U13(X1,X2,X3)
a__U14(X1,X2,X3) -> U14(X1,X2,X3)
a__U15(X1,X2) -> U15(X1,X2)
a__U16(X) -> U16(X)
a__U21(X1,X2) -> U21(X1,X2)
a__U22(X1,X2) -> U22(X1,X2)
a__U23(X) -> U23(X)
a__U31(X1,X2,X3) -> U31(X1,X2,X3)
a__U32(X1,X2,X3) -> U32(X1,X2,X3)
a__U33(X1,X2,X3) -> U33(X1,X2,X3)
a__U34(X1,X2,X3) -> U34(X1,X2,X3)
a__U35(X1,X2) -> U35(X1,X2)
a__U36(X) -> U36(X)
a__U41(X1,X2) -> U41(X1,X2)
a__U42(X) -> U42(X)
a__U51(X) -> U51(X)
a__U61(X1,X2) -> U61(X1,X2)
a__U62(X) -> U62(X)
a__U71(X1,X2) -> U71(X1,X2)
a__U72(X1,X2) -> U72(X1,X2)
a__U81(X1,X2,X3) -> U81(X1,X2,X3)
a__U82(X1,X2,X3) -> U82(X1,X2,X3)
a__U83(X1,X2,X3) -> U83(X1,X2,X3)
a__U84(X1,X2,X3) -> U84(X1,X2,X3)
a__U91(X1,X2) -> U91(X1,X2)
a__U92(X) -> U92(X)

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 MYNAT complete noand GM

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 MYNAT complete noand GM

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  a__U101(tt(), M, N) -> a__U102(a__isNatKind(M), M, N)
     , a__U102(tt(), M, N) -> a__U103(a__isNat(N), M, N)
     , a__U103(tt(), M, N) -> a__U104(a__isNatKind(N), M, N)
     , a__U104(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
     , a__U11(tt(), V1, V2) -> a__U12(a__isNatKind(V1), V1, V2)
     , a__U12(tt(), V1, V2) -> a__U13(a__isNatKind(V2), V1, V2)
     , a__U13(tt(), V1, V2) -> a__U14(a__isNatKind(V2), V1, V2)
     , a__U14(tt(), V1, V2) -> a__U15(a__isNat(V1), V2)
     , a__U15(tt(), V2) -> a__U16(a__isNat(V2))
     , a__U16(tt()) -> tt()
     , a__U21(tt(), V1) -> a__U22(a__isNatKind(V1), V1)
     , a__U22(tt(), V1) -> a__U23(a__isNat(V1))
     , a__U23(tt()) -> tt()
     , a__U31(tt(), V1, V2) -> a__U32(a__isNatKind(V1), V1, V2)
     , a__U32(tt(), V1, V2) -> a__U33(a__isNatKind(V2), V1, V2)
     , a__U33(tt(), V1, V2) -> a__U34(a__isNatKind(V2), V1, V2)
     , a__U34(tt(), V1, V2) -> a__U35(a__isNat(V1), V2)
     , a__U35(tt(), V2) -> a__U36(a__isNat(V2))
     , a__U36(tt()) -> tt()
     , a__U41(tt(), V2) -> a__U42(a__isNatKind(V2))
     , a__U42(tt()) -> tt()
     , a__U51(tt()) -> tt()
     , a__U61(tt(), V2) -> a__U62(a__isNatKind(V2))
     , a__U62(tt()) -> tt()
     , a__U71(tt(), N) -> a__U72(a__isNatKind(N), N)
     , a__U72(tt(), N) -> mark(N)
     , a__U81(tt(), M, N) -> a__U82(a__isNatKind(M), M, N)
     , a__U82(tt(), M, N) -> a__U83(a__isNat(N), M, N)
     , a__U83(tt(), M, N) -> a__U84(a__isNatKind(N), M, N)
     , a__U84(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
     , a__U91(tt(), N) -> a__U92(a__isNatKind(N))
     , a__U92(tt()) -> 0()
     , a__isNat(0()) -> tt()
     , a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2)
     , a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
     , a__isNat(x(V1, V2)) -> a__U31(a__isNatKind(V1), V1, V2)
     , a__isNatKind(0()) -> tt()
     , a__isNatKind(plus(V1, V2)) -> a__U41(a__isNatKind(V1), V2)
     , a__isNatKind(s(V1)) -> a__U51(a__isNatKind(V1))
     , a__isNatKind(x(V1, V2)) -> a__U61(a__isNatKind(V1), V2)
     , a__plus(N, 0()) -> a__U71(a__isNat(N), N)
     , a__plus(N, s(M)) -> a__U81(a__isNat(M), M, N)
     , a__x(N, 0()) -> a__U91(a__isNat(N), N)
     , a__x(N, s(M)) -> a__U101(a__isNat(M), M, N)
     , mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
     , mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
     , mark(isNatKind(X)) -> a__isNatKind(X)
     , mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
     , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
     , mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
     , mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
     , mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
     , mark(U15(X1, X2)) -> a__U15(mark(X1), X2)
     , mark(U16(X)) -> a__U16(mark(X))
     , mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
     , mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
     , mark(U23(X)) -> a__U23(mark(X))
     , mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
     , mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
     , mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
     , mark(U34(X1, X2, X3)) -> a__U34(mark(X1), X2, X3)
     , mark(U35(X1, X2)) -> a__U35(mark(X1), X2)
     , mark(U36(X)) -> a__U36(mark(X))
     , mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
     , mark(U42(X)) -> a__U42(mark(X))
     , mark(U51(X)) -> a__U51(mark(X))
     , mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
     , mark(U62(X)) -> a__U62(mark(X))
     , mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
     , mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
     , mark(U81(X1, X2, X3)) -> a__U81(mark(X1), X2, X3)
     , mark(U82(X1, X2, X3)) -> a__U82(mark(X1), X2, X3)
     , mark(U83(X1, X2, X3)) -> a__U83(mark(X1), X2, X3)
     , mark(U84(X1, X2, X3)) -> a__U84(mark(X1), X2, X3)
     , mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
     , mark(U92(X)) -> a__U92(mark(X))
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , a__U101(X1, X2, X3) -> U101(X1, X2, X3)
     , a__U102(X1, X2, X3) -> U102(X1, X2, X3)
     , a__isNatKind(X) -> isNatKind(X)
     , a__U103(X1, X2, X3) -> U103(X1, X2, X3)
     , a__isNat(X) -> isNat(X)
     , a__U104(X1, X2, X3) -> U104(X1, X2, X3)
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__x(X1, X2) -> x(X1, X2)
     , a__U11(X1, X2, X3) -> U11(X1, X2, X3)
     , a__U12(X1, X2, X3) -> U12(X1, X2, X3)
     , a__U13(X1, X2, X3) -> U13(X1, X2, X3)
     , a__U14(X1, X2, X3) -> U14(X1, X2, X3)
     , a__U15(X1, X2) -> U15(X1, X2)
     , a__U16(X) -> U16(X)
     , a__U21(X1, X2) -> U21(X1, X2)
     , a__U22(X1, X2) -> U22(X1, X2)
     , a__U23(X) -> U23(X)
     , a__U31(X1, X2, X3) -> U31(X1, X2, X3)
     , a__U32(X1, X2, X3) -> U32(X1, X2, X3)
     , a__U33(X1, X2, X3) -> U33(X1, X2, X3)
     , a__U34(X1, X2, X3) -> U34(X1, X2, X3)
     , a__U35(X1, X2) -> U35(X1, X2)
     , a__U36(X) -> U36(X)
     , a__U41(X1, X2) -> U41(X1, X2)
     , a__U42(X) -> U42(X)
     , a__U51(X) -> U51(X)
     , a__U61(X1, X2) -> U61(X1, X2)
     , a__U62(X) -> U62(X)
     , a__U71(X1, X2) -> U71(X1, X2)
     , a__U72(X1, X2) -> U72(X1, X2)
     , a__U81(X1, X2, X3) -> U81(X1, X2, X3)
     , a__U82(X1, X2, X3) -> U82(X1, X2, X3)
     , a__U83(X1, X2, X3) -> U83(X1, X2, X3)
     , a__U84(X1, X2, X3) -> U84(X1, X2, X3)
     , a__U91(X1, X2) -> U91(X1, X2)
     , a__U92(X) -> U92(X)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 MYNAT complete noand GM

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 MYNAT complete noand GM

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  a__U101(tt(), M, N) -> a__U102(a__isNatKind(M), M, N)
     , a__U102(tt(), M, N) -> a__U103(a__isNat(N), M, N)
     , a__U103(tt(), M, N) -> a__U104(a__isNatKind(N), M, N)
     , a__U104(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
     , a__U11(tt(), V1, V2) -> a__U12(a__isNatKind(V1), V1, V2)
     , a__U12(tt(), V1, V2) -> a__U13(a__isNatKind(V2), V1, V2)
     , a__U13(tt(), V1, V2) -> a__U14(a__isNatKind(V2), V1, V2)
     , a__U14(tt(), V1, V2) -> a__U15(a__isNat(V1), V2)
     , a__U15(tt(), V2) -> a__U16(a__isNat(V2))
     , a__U16(tt()) -> tt()
     , a__U21(tt(), V1) -> a__U22(a__isNatKind(V1), V1)
     , a__U22(tt(), V1) -> a__U23(a__isNat(V1))
     , a__U23(tt()) -> tt()
     , a__U31(tt(), V1, V2) -> a__U32(a__isNatKind(V1), V1, V2)
     , a__U32(tt(), V1, V2) -> a__U33(a__isNatKind(V2), V1, V2)
     , a__U33(tt(), V1, V2) -> a__U34(a__isNatKind(V2), V1, V2)
     , a__U34(tt(), V1, V2) -> a__U35(a__isNat(V1), V2)
     , a__U35(tt(), V2) -> a__U36(a__isNat(V2))
     , a__U36(tt()) -> tt()
     , a__U41(tt(), V2) -> a__U42(a__isNatKind(V2))
     , a__U42(tt()) -> tt()
     , a__U51(tt()) -> tt()
     , a__U61(tt(), V2) -> a__U62(a__isNatKind(V2))
     , a__U62(tt()) -> tt()
     , a__U71(tt(), N) -> a__U72(a__isNatKind(N), N)
     , a__U72(tt(), N) -> mark(N)
     , a__U81(tt(), M, N) -> a__U82(a__isNatKind(M), M, N)
     , a__U82(tt(), M, N) -> a__U83(a__isNat(N), M, N)
     , a__U83(tt(), M, N) -> a__U84(a__isNatKind(N), M, N)
     , a__U84(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
     , a__U91(tt(), N) -> a__U92(a__isNatKind(N))
     , a__U92(tt()) -> 0()
     , a__isNat(0()) -> tt()
     , a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2)
     , a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
     , a__isNat(x(V1, V2)) -> a__U31(a__isNatKind(V1), V1, V2)
     , a__isNatKind(0()) -> tt()
     , a__isNatKind(plus(V1, V2)) -> a__U41(a__isNatKind(V1), V2)
     , a__isNatKind(s(V1)) -> a__U51(a__isNatKind(V1))
     , a__isNatKind(x(V1, V2)) -> a__U61(a__isNatKind(V1), V2)
     , a__plus(N, 0()) -> a__U71(a__isNat(N), N)
     , a__plus(N, s(M)) -> a__U81(a__isNat(M), M, N)
     , a__x(N, 0()) -> a__U91(a__isNat(N), N)
     , a__x(N, s(M)) -> a__U101(a__isNat(M), M, N)
     , mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
     , mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
     , mark(isNatKind(X)) -> a__isNatKind(X)
     , mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
     , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
     , mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
     , mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
     , mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
     , mark(U15(X1, X2)) -> a__U15(mark(X1), X2)
     , mark(U16(X)) -> a__U16(mark(X))
     , mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
     , mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
     , mark(U23(X)) -> a__U23(mark(X))
     , mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
     , mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
     , mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
     , mark(U34(X1, X2, X3)) -> a__U34(mark(X1), X2, X3)
     , mark(U35(X1, X2)) -> a__U35(mark(X1), X2)
     , mark(U36(X)) -> a__U36(mark(X))
     , mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
     , mark(U42(X)) -> a__U42(mark(X))
     , mark(U51(X)) -> a__U51(mark(X))
     , mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
     , mark(U62(X)) -> a__U62(mark(X))
     , mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
     , mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
     , mark(U81(X1, X2, X3)) -> a__U81(mark(X1), X2, X3)
     , mark(U82(X1, X2, X3)) -> a__U82(mark(X1), X2, X3)
     , mark(U83(X1, X2, X3)) -> a__U83(mark(X1), X2, X3)
     , mark(U84(X1, X2, X3)) -> a__U84(mark(X1), X2, X3)
     , mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
     , mark(U92(X)) -> a__U92(mark(X))
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , a__U101(X1, X2, X3) -> U101(X1, X2, X3)
     , a__U102(X1, X2, X3) -> U102(X1, X2, X3)
     , a__isNatKind(X) -> isNatKind(X)
     , a__U103(X1, X2, X3) -> U103(X1, X2, X3)
     , a__isNat(X) -> isNat(X)
     , a__U104(X1, X2, X3) -> U104(X1, X2, X3)
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__x(X1, X2) -> x(X1, X2)
     , a__U11(X1, X2, X3) -> U11(X1, X2, X3)
     , a__U12(X1, X2, X3) -> U12(X1, X2, X3)
     , a__U13(X1, X2, X3) -> U13(X1, X2, X3)
     , a__U14(X1, X2, X3) -> U14(X1, X2, X3)
     , a__U15(X1, X2) -> U15(X1, X2)
     , a__U16(X) -> U16(X)
     , a__U21(X1, X2) -> U21(X1, X2)
     , a__U22(X1, X2) -> U22(X1, X2)
     , a__U23(X) -> U23(X)
     , a__U31(X1, X2, X3) -> U31(X1, X2, X3)
     , a__U32(X1, X2, X3) -> U32(X1, X2, X3)
     , a__U33(X1, X2, X3) -> U33(X1, X2, X3)
     , a__U34(X1, X2, X3) -> U34(X1, X2, X3)
     , a__U35(X1, X2) -> U35(X1, X2)
     , a__U36(X) -> U36(X)
     , a__U41(X1, X2) -> U41(X1, X2)
     , a__U42(X) -> U42(X)
     , a__U51(X) -> U51(X)
     , a__U61(X1, X2) -> U61(X1, X2)
     , a__U62(X) -> U62(X)
     , a__U71(X1, X2) -> U71(X1, X2)
     , a__U72(X1, X2) -> U72(X1, X2)
     , a__U81(X1, X2, X3) -> U81(X1, X2, X3)
     , a__U82(X1, X2, X3) -> U82(X1, X2, X3)
     , a__U83(X1, X2, X3) -> U83(X1, X2, X3)
     , a__U84(X1, X2, X3) -> U84(X1, X2, X3)
     , a__U91(X1, X2) -> U91(X1, X2)
     , a__U92(X) -> U92(X)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds