TRS Contextsensitive pair #487092653

details

property	value
status	complete
benchmark	MYNAT_nokinds.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	Maude_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.13648 seconds
cpu usage	5.76703
user time	5.52112
system time	0.245909
max virtual memory	1.8475704E7
max residence set size	454900.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given CSR could be proven:

(0) CSR
(1) CSDependencyPairsProof [EQUIVALENT, 0 ms]
(2) QCSDP
(3) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QCSDP
        (6) QCSDPReductionPairProof [EQUIVALENT, 171 ms]
        (7) QCSDP
        (8) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (9) TRUE
    (10) QCSDP
        (11) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (12) QCSDP
        (13) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (14) TRUE
    (15) QCSDP
        (16) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (17) QCSDP
        (18) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (19) TRUE


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

(0)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   U11(tt, N) -> N
   U21(tt, M, N) -> s(plus(N, M))
   U31(tt) -> 0
   U41(tt, M, N) -> plus(x(N, M), N)
   and(tt, X) -> X
   isNat(0) -> tt
   isNat(plus(V1, V2)) -> and(isNat(V1), isNat(V2))
   isNat(s(V1)) -> isNat(V1)
   isNat(x(V1, V2)) -> and(isNat(V1), isNat(V2))
   plus(N, 0) -> U11(isNat(N), N)
   plus(N, s(M)) -> U21(and(isNat(M), isNat(N)), M, N)
   x(N, 0) -> U31(isNat(N))
   x(N, s(M)) -> U41(and(isNat(M), isNat(N)), M, N)

The replacement map contains the following entries:

U11: {1}
tt: empty set
U21: {1}
s: {1}
plus: {1, 2}
U31: {1}
0: empty set
U41: {1}
x: {1, 2}
and: {1}
isNat: empty set

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

(1) CSDependencyPairsProof (EQUIVALENT)
Using Improved CS-DPs [LPAR08] we result in the following initial Q-CSDP problem.
----------------------------------------

(2)
Obligation:
Q-restricted context-sensitive dependency pair problem:
The symbols in {s_1, plus_2, U31_1, x_2, PLUS_2, X_2, U31'_1} are replacing on all positions.
For all symbols f in {U11_2, U21_3, U41_3, and_2, U21'_3, U41'_3, AND_2, U11'_2} we have mu(f) = {1}.
The symbols in {isNat_1, ISNAT_1, U_1} are not replacing on any position.

The ordinary context-sensitive dependency pairs DP_o are:
   U21'(tt, M, N) -> PLUS(N, M)
   U41'(tt, M, N) -> PLUS(x(N, M), N)
   U41'(tt, M, N) -> X(N, M)
   ISNAT(plus(V1, V2)) -> AND(isNat(V1), isNat(V2))
   ISNAT(plus(V1, V2)) -> ISNAT(V1)
   ISNAT(s(V1)) -> ISNAT(V1)
   ISNAT(x(V1, V2)) -> AND(isNat(V1), isNat(V2))
   ISNAT(x(V1, V2)) -> ISNAT(V1)
   PLUS(N, 0) -> U11'(isNat(N), N)
   PLUS(N, 0) -> ISNAT(N)
   PLUS(N, s(M)) -> U21'(and(isNat(M), isNat(N)), M, N)
   PLUS(N, s(M)) -> AND(isNat(M), isNat(N))
   PLUS(N, s(M)) -> ISNAT(M)
   X(N, 0) -> U31'(isNat(N))
   X(N, 0) -> ISNAT(N)
   X(N, s(M)) -> U41'(and(isNat(M), isNat(N)), M, N)
   X(N, s(M)) -> AND(isNat(M), isNat(N))
   X(N, s(M)) -> ISNAT(M)

The collapsing dependency pairs are DP_c:
   U11'(tt, N) -> N
   U21'(tt, M, N) -> N

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