TRS Conte Sensi 17651 pair #381733293

details

property	value
status	complete
benchmark	MYNAT_nosorts.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n016.star.cs.uiowa.edu
space	Maude_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.21655392647 seconds
cpu usage	3.237076284
max memory	1.98139904E8

stage attributes

key	value
output-size	6653
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 23 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:

   and(tt, X) -> X
   plus(N, 0) -> N
   plus(N, s(M)) -> s(plus(N, M))
   x(N, 0) -> 0
   x(N, s(M)) -> plus(x(N, M), N)

The replacement map contains the following entries:

and: {1}
tt: empty set
plus: {1, 2}
0: empty set
s: {1}
x: {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:

   and(tt, X) -> X
   plus(N, 0) -> N
   plus(N, s(M)) -> s(plus(N, M))
   x(N, 0) -> 0
   x(N, s(M)) -> plus(x(N, M), N)

The replacement map contains the following entries:

and: {1}
tt: empty set
plus: {1, 2}
0: empty set
s: {1}
x: {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 {plus_2, s_1, x_2, PLUS_2, X_2} are replacing on all positions.
For all symbols f in {and_2, AND_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:
   PLUS(N, s(M)) -> PLUS(N, M)
   X(N, s(M)) -> PLUS(x(N, M), N)
   X(N, s(M)) -> X(N, M)

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