TRS Standard pair #516964110

details

property	value
status	complete
benchmark	21.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n113.star.cs.uiowa.edu
space	Der95

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.21612715721 seconds
cpu usage	5.717586114
max memory	4.68922368E8

stage attributes

key	value
output-size	10275
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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 w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) Overlay + Local Confluence [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 0 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QReductionProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QReductionProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QReductionProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) MRRProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) DependencyGraphProof [EQUIVALENT, 0 ms]
        (29) TRUE


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

(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   p(s(x)) -> x
   fact(0) -> s(0)
   fact(s(x)) -> *(s(x), fact(p(s(x))))
   *(0, y) -> 0
   *(s(x), y) -> +(*(x, y), y)
   +(x, 0) -> x
   +(x, s(y)) -> s(+(x, y))

Q is empty.

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

(1) Overlay + Local Confluence (EQUIVALENT)
The TRS is overlay and locally confluent. By [NOC] we can switch to innermost.
----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   p(s(x)) -> x
   fact(0) -> s(0)
   fact(s(x)) -> *(s(x), fact(p(s(x))))
   *(0, y) -> 0
   *(s(x), y) -> +(*(x, y), y)
   +(x, 0) -> x
   +(x, s(y)) -> s(+(x, y))

The set Q consists of the following terms:

   p(s(x0))
   fact(0)
   fact(s(x0))
   *(0, x0)
   *(s(x0), x1)
   +(x0, 0)
   +(x0, s(x1))


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

(3) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(4)
Obligation:

popout

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

job log

popout

actions all output return to TRS Standard