TRS Contextsensitive pair #487092553

details

property	value
status	complete
benchmark	Ex4_7_37_Bor03.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.73889 seconds
cpu usage	4.21831
user time	4.04648
system time	0.171831
max virtual memory	5.5200052E7
max residence set size	297544.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (7) QCSDP
        (8) PIsEmptyProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QCSDP
        (11) QCSDPReductionPairProof [EQUIVALENT, 41 ms]
        (12) QCSDP
        (13) PIsEmptyProof [EQUIVALENT, 0 ms]
        (14) YES
    (15) QCSDP
        (16) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (17) QCSDP
        (18) PIsEmptyProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QCSDP
        (21) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (22) QCSDP
        (23) PIsEmptyProof [EQUIVALENT, 0 ms]
        (24) YES


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

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

   from(X) -> cons(X, from(s(X)))
   sel(0, cons(X, XS)) -> X
   sel(s(N), cons(X, XS)) -> sel(N, XS)
   minus(X, 0) -> 0
   minus(s(X), s(Y)) -> minus(X, Y)
   quot(0, s(Y)) -> 0
   quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y)))
   zWquot(XS, nil) -> nil
   zWquot(nil, XS) -> nil
   zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), zWquot(XS, YS))

The replacement map contains the following entries:

from: {1}
cons: {1}
s: {1}
sel: {1, 2}
0: empty set
minus: {1, 2}
quot: {1, 2}
zWquot: {1, 2}
nil: 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 {from_1, s_1, sel_2, minus_2, quot_2, zWquot_2, SEL_2, MINUS_2, QUOT_2, ZWQUOT_2, FROM_1} are replacing on all positions.
For all symbols f in {cons_2} we have mu(f) = {1}.
The symbols in {U_1} are not replacing on any position.

The ordinary context-sensitive dependency pairs DP_o are:
   SEL(s(N), cons(X, XS)) -> SEL(N, XS)
   MINUS(s(X), s(Y)) -> MINUS(X, Y)
   QUOT(s(X), s(Y)) -> QUOT(minus(X, Y), s(Y))
   QUOT(s(X), s(Y)) -> MINUS(X, Y)
   ZWQUOT(cons(X, XS), cons(Y, YS)) -> QUOT(X, Y)

The collapsing dependency pairs are DP_c:
   SEL(s(N), cons(X, XS)) -> XS


The hidden terms of R are:

   from(s(x0))
   zWquot(x0, x1)

Every hiding context is built from:
   aprove.DPFramework.CSDPProblem.QCSDPProblem$1@165e0ef2
   aprove.DPFramework.CSDPProblem.QCSDPProblem$1@535c825d
   aprove.DPFramework.CSDPProblem.QCSDPProblem$1@7c7977c1

Hence, the new unhiding pairs DP_u are :
   SEL(s(N), cons(X, XS)) -> U(XS)

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