Problem Transformed CSR 04 PEANO complete C

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 PEANO complete C

stdout:

MAYBE

Problem:
active(U11(tt(),V1,V2)) -> mark(U12(isNat(V1),V2))
active(U12(tt(),V2)) -> mark(U13(isNat(V2)))
active(U13(tt())) -> mark(tt())
active(U21(tt(),V1)) -> mark(U22(isNat(V1)))
active(U22(tt())) -> mark(tt())
active(U31(tt(),N)) -> mark(N)
active(U41(tt(),M,N)) -> mark(s(plus(N,M)))
active(and(tt(),X)) -> mark(X)
active(isNat(0())) -> mark(tt())
active(isNat(plus(V1,V2))) -> mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))
active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
active(isNatKind(0())) -> mark(tt())
active(isNatKind(plus(V1,V2))) -> mark(and(isNatKind(V1),isNatKind(V2)))
active(isNatKind(s(V1))) -> mark(isNatKind(V1))
active(plus(N,0())) -> mark(U31(and(isNat(N),isNatKind(N)),N))
active(plus(N,s(M))) -> mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))
active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
active(U12(X1,X2)) -> U12(active(X1),X2)
active(U13(X)) -> U13(active(X))
active(U21(X1,X2)) -> U21(active(X1),X2)
active(U22(X)) -> U22(active(X))
active(U31(X1,X2)) -> U31(active(X1),X2)
active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
active(s(X)) -> s(active(X))
active(plus(X1,X2)) -> plus(active(X1),X2)
active(plus(X1,X2)) -> plus(X1,active(X2))
active(and(X1,X2)) -> and(active(X1),X2)
U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
U12(mark(X1),X2) -> mark(U12(X1,X2))
U13(mark(X)) -> mark(U13(X))
U21(mark(X1),X2) -> mark(U21(X1,X2))
U22(mark(X)) -> mark(U22(X))
U31(mark(X1),X2) -> mark(U31(X1,X2))
U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
s(mark(X)) -> mark(s(X))
plus(mark(X1),X2) -> mark(plus(X1,X2))
plus(X1,mark(X2)) -> mark(plus(X1,X2))
and(mark(X1),X2) -> mark(and(X1,X2))
proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
proper(tt()) -> ok(tt())
proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
proper(isNat(X)) -> isNat(proper(X))
proper(U13(X)) -> U13(proper(X))
proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
proper(U22(X)) -> U22(proper(X))
proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
proper(s(X)) -> s(proper(X))
proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
proper(and(X1,X2)) -> and(proper(X1),proper(X2))
proper(0()) -> ok(0())
proper(isNatKind(X)) -> isNatKind(proper(X))
U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
isNat(ok(X)) -> ok(isNat(X))
U13(ok(X)) -> ok(U13(X))
U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
U22(ok(X)) -> ok(U22(X))
U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
s(ok(X)) -> ok(s(X))
plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
and(ok(X1),ok(X2)) -> ok(and(X1,X2))
isNatKind(ok(X)) -> ok(isNatKind(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 PEANO complete C

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 PEANO complete C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2))
     , active(U12(tt(), V2)) -> mark(U13(isNat(V2)))
     , active(U13(tt())) -> mark(tt())
     , active(U21(tt(), V1)) -> mark(U22(isNat(V1)))
     , active(U22(tt())) -> mark(tt())
     , active(U31(tt(), N)) -> mark(N)
     , active(U41(tt(), M, N)) -> mark(s(plus(N, M)))
     , active(and(tt(), X)) -> mark(X)
     , active(isNat(0())) -> mark(tt())
     , active(isNat(plus(V1, V2))) ->
       mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2))
     , active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
     , active(isNatKind(0())) -> mark(tt())
     , active(isNatKind(plus(V1, V2))) ->
       mark(and(isNatKind(V1), isNatKind(V2)))
     , active(isNatKind(s(V1))) -> mark(isNatKind(V1))
     , active(plus(N, 0())) -> mark(U31(and(isNat(N), isNatKind(N)), N))
     , active(plus(N, s(M))) ->
       mark(U41(and(and(isNat(M), isNatKind(M)),
                    and(isNat(N), isNatKind(N))),
                M,
                N))
     , active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
     , active(U12(X1, X2)) -> U12(active(X1), X2)
     , active(U13(X)) -> U13(active(X))
     , active(U21(X1, X2)) -> U21(active(X1), X2)
     , active(U22(X)) -> U22(active(X))
     , active(U31(X1, X2)) -> U31(active(X1), X2)
     , active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
     , active(s(X)) -> s(active(X))
     , active(plus(X1, X2)) -> plus(active(X1), X2)
     , active(plus(X1, X2)) -> plus(X1, active(X2))
     , active(and(X1, X2)) -> and(active(X1), X2)
     , U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3))
     , U12(mark(X1), X2) -> mark(U12(X1, X2))
     , U13(mark(X)) -> mark(U13(X))
     , U21(mark(X1), X2) -> mark(U21(X1, X2))
     , U22(mark(X)) -> mark(U22(X))
     , U31(mark(X1), X2) -> mark(U31(X1, X2))
     , U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3))
     , s(mark(X)) -> mark(s(X))
     , plus(mark(X1), X2) -> mark(plus(X1, X2))
     , plus(X1, mark(X2)) -> mark(plus(X1, X2))
     , and(mark(X1), X2) -> mark(and(X1, X2))
     , proper(U11(X1, X2, X3)) ->
       U11(proper(X1), proper(X2), proper(X3))
     , proper(tt()) -> ok(tt())
     , proper(U12(X1, X2)) -> U12(proper(X1), proper(X2))
     , proper(isNat(X)) -> isNat(proper(X))
     , proper(U13(X)) -> U13(proper(X))
     , proper(U21(X1, X2)) -> U21(proper(X1), proper(X2))
     , proper(U22(X)) -> U22(proper(X))
     , proper(U31(X1, X2)) -> U31(proper(X1), proper(X2))
     , proper(U41(X1, X2, X3)) ->
       U41(proper(X1), proper(X2), proper(X3))
     , proper(s(X)) -> s(proper(X))
     , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
     , proper(and(X1, X2)) -> and(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(isNatKind(X)) -> isNatKind(proper(X))
     , U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3))
     , U12(ok(X1), ok(X2)) -> ok(U12(X1, X2))
     , isNat(ok(X)) -> ok(isNat(X))
     , U13(ok(X)) -> ok(U13(X))
     , U21(ok(X1), ok(X2)) -> ok(U21(X1, X2))
     , U22(ok(X)) -> ok(U22(X))
     , U31(ok(X1), ok(X2)) -> ok(U31(X1, X2))
     , U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3))
     , s(ok(X)) -> ok(s(X))
     , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
     , and(ok(X1), ok(X2)) -> ok(and(X1, X2))
     , isNatKind(ok(X)) -> ok(isNatKind(X))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 PEANO complete C

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 PEANO complete C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2))
     , active(U12(tt(), V2)) -> mark(U13(isNat(V2)))
     , active(U13(tt())) -> mark(tt())
     , active(U21(tt(), V1)) -> mark(U22(isNat(V1)))
     , active(U22(tt())) -> mark(tt())
     , active(U31(tt(), N)) -> mark(N)
     , active(U41(tt(), M, N)) -> mark(s(plus(N, M)))
     , active(and(tt(), X)) -> mark(X)
     , active(isNat(0())) -> mark(tt())
     , active(isNat(plus(V1, V2))) ->
       mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2))
     , active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
     , active(isNatKind(0())) -> mark(tt())
     , active(isNatKind(plus(V1, V2))) ->
       mark(and(isNatKind(V1), isNatKind(V2)))
     , active(isNatKind(s(V1))) -> mark(isNatKind(V1))
     , active(plus(N, 0())) -> mark(U31(and(isNat(N), isNatKind(N)), N))
     , active(plus(N, s(M))) ->
       mark(U41(and(and(isNat(M), isNatKind(M)),
                    and(isNat(N), isNatKind(N))),
                M,
                N))
     , active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
     , active(U12(X1, X2)) -> U12(active(X1), X2)
     , active(U13(X)) -> U13(active(X))
     , active(U21(X1, X2)) -> U21(active(X1), X2)
     , active(U22(X)) -> U22(active(X))
     , active(U31(X1, X2)) -> U31(active(X1), X2)
     , active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
     , active(s(X)) -> s(active(X))
     , active(plus(X1, X2)) -> plus(active(X1), X2)
     , active(plus(X1, X2)) -> plus(X1, active(X2))
     , active(and(X1, X2)) -> and(active(X1), X2)
     , U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3))
     , U12(mark(X1), X2) -> mark(U12(X1, X2))
     , U13(mark(X)) -> mark(U13(X))
     , U21(mark(X1), X2) -> mark(U21(X1, X2))
     , U22(mark(X)) -> mark(U22(X))
     , U31(mark(X1), X2) -> mark(U31(X1, X2))
     , U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3))
     , s(mark(X)) -> mark(s(X))
     , plus(mark(X1), X2) -> mark(plus(X1, X2))
     , plus(X1, mark(X2)) -> mark(plus(X1, X2))
     , and(mark(X1), X2) -> mark(and(X1, X2))
     , proper(U11(X1, X2, X3)) ->
       U11(proper(X1), proper(X2), proper(X3))
     , proper(tt()) -> ok(tt())
     , proper(U12(X1, X2)) -> U12(proper(X1), proper(X2))
     , proper(isNat(X)) -> isNat(proper(X))
     , proper(U13(X)) -> U13(proper(X))
     , proper(U21(X1, X2)) -> U21(proper(X1), proper(X2))
     , proper(U22(X)) -> U22(proper(X))
     , proper(U31(X1, X2)) -> U31(proper(X1), proper(X2))
     , proper(U41(X1, X2, X3)) ->
       U41(proper(X1), proper(X2), proper(X3))
     , proper(s(X)) -> s(proper(X))
     , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
     , proper(and(X1, X2)) -> and(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(isNatKind(X)) -> isNatKind(proper(X))
     , U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3))
     , U12(ok(X1), ok(X2)) -> ok(U12(X1, X2))
     , isNat(ok(X)) -> ok(isNat(X))
     , U13(ok(X)) -> ok(U13(X))
     , U21(ok(X1), ok(X2)) -> ok(U21(X1, X2))
     , U22(ok(X)) -> ok(U22(X))
     , U31(ok(X1), ok(X2)) -> ok(U31(X1, X2))
     , U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3))
     , s(ok(X)) -> ok(s(X))
     , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
     , and(ok(X1), ok(X2)) -> ok(and(X1, X2))
     , isNatKind(ok(X)) -> ok(isNatKind(X))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds