TRS Stand 20472 pair #381709962

details

property	value
status	complete
benchmark	cade14.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n023.star.cs.uiowa.edu
space	GTSSK07

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	6.48813796043 seconds
cpu usage	10.912673692
max memory	5.44256E8

stage attributes

key	value
output-size	38941
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) Overlay + Local Confluence [EQUIVALENT, 15 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, 1182 ms]
        (27) QDP
        (28) DependencyGraphProof [EQUIVALENT, 0 ms]
        (29) TRUE


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

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

   diff(x, y) -> cond1(equal(x, y), x, y)
   cond1(true, x, y) -> 0
   cond1(false, x, y) -> cond2(gt(x, y), x, y)
   cond2(true, x, y) -> s(diff(x, s(y)))
   cond2(false, x, y) -> s(diff(s(x), y))
   gt(0, v) -> false
   gt(s(u), 0) -> true
   gt(s(u), s(v)) -> gt(u, v)
   equal(0, 0) -> true
   equal(s(x), 0) -> false
   equal(0, s(y)) -> false
   equal(s(x), s(y)) -> equal(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:

   diff(x, y) -> cond1(equal(x, y), x, y)
   cond1(true, x, y) -> 0
   cond1(false, x, y) -> cond2(gt(x, y), x, y)
   cond2(true, x, y) -> s(diff(x, s(y)))
   cond2(false, x, y) -> s(diff(s(x), y))
   gt(0, v) -> false
   gt(s(u), 0) -> true
   gt(s(u), s(v)) -> gt(u, v)
   equal(0, 0) -> true
   equal(s(x), 0) -> false
   equal(0, s(y)) -> false
   equal(s(x), s(y)) -> equal(x, y)

The set Q consists of the following terms:

   diff(x0, x1)
   cond1(true, x0, x1)
   cond1(false, x0, x1)
   cond2(true, x0, x1)
   cond2(false, x0, x1)
   gt(0, x0)
   gt(s(x0), 0)

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