TRS Standard pair #516968005

details

property	value
status	complete
benchmark	cade06.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n067.star.cs.uiowa.edu
space	GTSSK07

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	3.04655098915 seconds
cpu usage	8.384947971
max memory	5.52804352E8

stage attributes

key	value
output-size	39915
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) AAECC Innermost [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) NonInfProof [EQUIVALENT, 132 ms]
        (27) QDP
        (28) PisEmptyProof [EQUIVALENT, 0 ms]
        (29) YES


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

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

   f(true, x, y, z) -> f(gt(x, plus(y, z)), x, s(y), z)
   f(true, x, y, z) -> f(gt(x, plus(y, z)), x, y, s(z))
   plus(n, 0) -> n
   plus(n, s(m)) -> s(plus(n, m))
   gt(0, v) -> false
   gt(s(u), 0) -> true
   gt(s(u), s(v)) -> gt(u, v)

Q is empty.

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

(1) AAECC Innermost (EQUIVALENT)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is 
   plus(n, 0) -> n
   plus(n, s(m)) -> s(plus(n, m))
   gt(0, v) -> false
   gt(s(u), 0) -> true
   gt(s(u), s(v)) -> gt(u, v)

The TRS R 2 is 
   f(true, x, y, z) -> f(gt(x, plus(y, z)), x, s(y), z)
   f(true, x, y, z) -> f(gt(x, plus(y, z)), x, y, s(z))

The signature Sigma is {f_4}
----------------------------------------

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

   f(true, x, y, z) -> f(gt(x, plus(y, z)), x, s(y), z)
   f(true, x, y, z) -> f(gt(x, plus(y, z)), x, y, s(z))
   plus(n, 0) -> n
   plus(n, s(m)) -> s(plus(n, m))
   gt(0, v) -> false
   gt(s(u), 0) -> true
   gt(s(u), s(v)) -> gt(u, v)

The set Q consists of the following terms:

   f(true, x0, x1, x2)
   plus(x0, 0)
   plus(x0, s(x1))
   gt(0, x0)
   gt(s(x0), 0)
   gt(s(x0), s(x1))

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