TRS Contextsensitive pair #487092523

details

property	value
status	complete
benchmark	Ex1_Luc02b.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	CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.52864 seconds
cpu usage	3.39716
user time	3.26009
system time	0.137062
max virtual memory	1.8343148E7
max residence set size	213608.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) CSRInnermostProof [EQUIVALENT, 0 ms]
(2) CSR
(3) CSDependencyPairsProof [EQUIVALENT, 0 ms]
(4) QCSDP
(5) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QCSDP
        (8) QCSDPSubtermProof [EQUIVALENT, 10 ms]
        (9) QCSDP
        (10) PIsEmptyProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QCSDP
        (13) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (14) QCSDP
        (15) PIsEmptyProof [EQUIVALENT, 0 ms]
        (16) YES


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

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

   from(X) -> cons(X, from(s(X)))
   first(0, Z) -> nil
   first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
   sel(0, cons(X, Z)) -> X
   sel(s(X), cons(Y, Z)) -> sel(X, Z)

The replacement map contains the following entries:

from: {1}
cons: {1}
s: {1}
first: {1, 2}
0: empty set
nil: empty set
sel: {1, 2}

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

(1) CSRInnermostProof (EQUIVALENT)
The CSR is orthogonal. By [CS_Inn] we can switch to innermost.
----------------------------------------

(2)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   from(X) -> cons(X, from(s(X)))
   first(0, Z) -> nil
   first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
   sel(0, cons(X, Z)) -> X
   sel(s(X), cons(Y, Z)) -> sel(X, Z)

The replacement map contains the following entries:

from: {1}
cons: {1}
s: {1}
first: {1, 2}
0: empty set
nil: empty set
sel: {1, 2}


Innermost Strategy.

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

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

(4)
Obligation:
Q-restricted context-sensitive dependency pair problem:
The symbols in {from_1, s_1, first_2, sel_2, SEL_2, FROM_1, FIRST_2} 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(X), cons(Y, Z)) -> SEL(X, Z)

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


The hidden terms of R are:

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to TRS Contextsensitive