TRS Standard pair #615302287

details

property	value
status	complete
benchmark	PEANO_nokinds-noand_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n054.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	3.19664287567 seconds
cpu usage	7.556694501
max memory	4.23067648E8

stage attributes

key	value
output-size	16792
starexec-result	"YES"

output

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


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 5 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) QDP
(5) QDPOrderProof [EQUIVALENT, 91 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QDP
        (10) QDPOrderProof [EQUIVALENT, 36 ms]
        (11) QDP
        (12) PisEmptyProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) QDPOrderProof [EQUIVALENT, 37 ms]
        (16) QDP
        (17) DependencyGraphProof [EQUIVALENT, 0 ms]
        (18) TRUE


----------------------------------------

(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   U11(tt, V2) -> U12(isNat(activate(V2)))
   U12(tt) -> tt
   U21(tt) -> tt
   U31(tt, N) -> activate(N)
   U41(tt, M, N) -> U42(isNat(activate(N)), activate(M), activate(N))
   U42(tt, M, N) -> s(plus(activate(N), activate(M)))
   isNat(n__0) -> tt
   isNat(n__plus(V1, V2)) -> U11(isNat(activate(V1)), activate(V2))
   isNat(n__s(V1)) -> U21(isNat(activate(V1)))
   plus(N, 0) -> U31(isNat(N), N)
   plus(N, s(M)) -> U41(isNat(M), M, N)
   0 -> n__0
   plus(X1, X2) -> n__plus(X1, X2)
   s(X) -> n__s(X)
   activate(n__0) -> 0
   activate(n__plus(X1, X2)) -> plus(X1, X2)
   activate(n__s(X)) -> s(X)
   activate(X) -> X

Q is empty.

----------------------------------------

(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(2)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   U11^1(tt, V2) -> U12^1(isNat(activate(V2)))
   U11^1(tt, V2) -> ISNAT(activate(V2))
   U11^1(tt, V2) -> ACTIVATE(V2)
   U31^1(tt, N) -> ACTIVATE(N)
   U41^1(tt, M, N) -> U42^1(isNat(activate(N)), activate(M), activate(N))
   U41^1(tt, M, N) -> ISNAT(activate(N))
   U41^1(tt, M, N) -> ACTIVATE(N)
   U41^1(tt, M, N) -> ACTIVATE(M)
   U42^1(tt, M, N) -> S(plus(activate(N), activate(M)))
   U42^1(tt, M, N) -> PLUS(activate(N), activate(M))
   U42^1(tt, M, N) -> ACTIVATE(N)
   U42^1(tt, M, N) -> ACTIVATE(M)
   ISNAT(n__plus(V1, V2)) -> U11^1(isNat(activate(V1)), activate(V2))
   ISNAT(n__plus(V1, V2)) -> ISNAT(activate(V1))
   ISNAT(n__plus(V1, V2)) -> ACTIVATE(V1)
   ISNAT(n__plus(V1, V2)) -> ACTIVATE(V2)
   ISNAT(n__s(V1)) -> U21^1(isNat(activate(V1)))
   ISNAT(n__s(V1)) -> ISNAT(activate(V1))
   ISNAT(n__s(V1)) -> ACTIVATE(V1)
   PLUS(N, 0) -> U31^1(isNat(N), N)
   PLUS(N, 0) -> ISNAT(N)
   PLUS(N, s(M)) -> U41^1(isNat(M), M, N)
   PLUS(N, s(M)) -> ISNAT(M)
   ACTIVATE(n__0) -> 0^1
   ACTIVATE(n__plus(X1, X2)) -> PLUS(X1, X2)
   ACTIVATE(n__s(X)) -> S(X)

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