TRS Stand 20472 pair #381710802

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	n095.star.cs.uiowa.edu
space	GTSSK07

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.47186899185 seconds
cpu usage	5.985832883
max memory	3.62528768E8

stage attributes

key	value
output-size	39922
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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 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, 104 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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