TRS Contextsensitive pair #487092509

details

property	value
status	complete
benchmark	Ex1_2_Luc02c.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.4397 seconds
cpu usage	3.09398
user time	2.96871
system time	0.125272
max virtual memory	1.8343376E7
max residence set size	206352.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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


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

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

   2nd(cons(X, cons(Y, Z))) -> Y
   from(X) -> cons(X, from(s(X)))

The replacement map contains the following entries:

2nd: {1}
cons: {1}
from: {1}
s: {1}

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

(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:

   2nd(cons(X, cons(Y, Z))) -> Y
   from(X) -> cons(X, from(s(X)))

The replacement map contains the following entries:

2nd: {1}
cons: {1}
from: {1}
s: {1}


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 {2nd_1, from_1, s_1, 2ND_1, 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 collapsing dependency pairs are DP_c:
   2ND(cons(X, cons(Y, Z))) -> Y


The hidden terms of R are:

   from(s(x0))

Every hiding context is built from:
   aprove.DPFramework.CSDPProblem.QCSDPProblem$1@6e914b66
   aprove.DPFramework.CSDPProblem.QCSDPProblem$1@46a6d3f8

Hence, the new unhiding pairs DP_u are :
   2ND(cons(X, cons(Y, Z))) -> U(Y)
   U(s(x_0)) -> U(x_0)
   U(from(x_0)) -> U(x_0)
   U(from(s(x0))) -> FROM(s(x0))

The TRS R consists of the following rules:

   2nd(cons(X, cons(Y, Z))) -> Y
   from(X) -> cons(X, from(s(X)))

The set Q consists of the following terms:

   2nd(cons(x0, cons(x1, x2)))

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