TRS Context Sensitive pair #516978889

details

property	value
status	complete
benchmark	MYNAT_nosorts-noand.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n092.star.cs.uiowa.edu
space	Maude_06

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.10037183762 seconds
cpu usage	5.401146149
max memory	4.8525312E8

stage attributes

key	value
output-size	8979
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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, 0 ms]
        (9) QCSDP
        (10) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (11) TRUE
    (12) QCSDP
        (13) QCSDPSubtermProof [EQUIVALENT, 2 ms]
        (14) QCSDP
        (15) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (16) TRUE


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

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

   U11(tt, M, N) -> U12(tt, M, N)
   U12(tt, M, N) -> s(plus(N, M))
   U21(tt, M, N) -> U22(tt, M, N)
   U22(tt, M, N) -> plus(x(N, M), N)
   plus(N, 0) -> N
   plus(N, s(M)) -> U11(tt, M, N)
   x(N, 0) -> 0
   x(N, s(M)) -> U21(tt, M, N)

The replacement map contains the following entries:

U11: {1}
tt: empty set
U12: {1}
s: {1}
plus: {1, 2}
U21: {1}
U22: {1}
x: {1, 2}
0: empty set

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

(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:

   U11(tt, M, N) -> U12(tt, M, N)
   U12(tt, M, N) -> s(plus(N, M))
   U21(tt, M, N) -> U22(tt, M, N)
   U22(tt, M, N) -> plus(x(N, M), N)
   plus(N, 0) -> N
   plus(N, s(M)) -> U11(tt, M, N)
   x(N, 0) -> 0
   x(N, s(M)) -> U21(tt, M, N)

The replacement map contains the following entries:

U11: {1}
tt: empty set
U12: {1}
s: {1}
plus: {1, 2}
U21: {1}
U22: {1}
x: {1, 2}
0: empty set


Innermost Strategy.

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

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