TRS Context Sensitive pair #516978897

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	n095.star.cs.uiowa.edu
space	Maude_06

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	10.3222198486 seconds
cpu usage	19.554023737
max memory	1.425145856E9

stage attributes

key	value
output-size	13127
starexec-result	YES

output

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


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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, 173 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)

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