TRS Stand 20472 pair #381710130

details

property	value
status	complete
benchmark	tower.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n003.star.cs.uiowa.edu
space	AProVE_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.12616205215 seconds
cpu usage	5.017205188
max memory	2.87383552E8

stage attributes

key	value
output-size	23004
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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


YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) MRRProof [EQUIVALENT, 14 ms]
        (20) QDP
        (21) QDPOrderProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) PisEmptyProof [EQUIVALENT, 0 ms]
        (24) YES
    (25) QDP
        (26) UsableRulesProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) QReductionProof [EQUIVALENT, 0 ms]
        (29) QDP
        (30) MRRProof [EQUIVALENT, 9 ms]
        (31) QDP
        (32) QDPOrderProof [EQUIVALENT, 11 ms]
        (33) QDP
        (34) PisEmptyProof [EQUIVALENT, 0 ms]
        (35) YES
    (36) QDP
        (37) UsableRulesProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) QReductionProof [EQUIVALENT, 0 ms]
        (40) QDP
        (41) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (42) YES
    (43) QDP
        (44) UsableRulesProof [EQUIVALENT, 0 ms]
        (45) QDP
        (46) QReductionProof [EQUIVALENT, 0 ms]
        (47) QDP
        (48) QDPOrderProof [EQUIVALENT, 0 ms]
        (49) QDP
        (50) PisEmptyProof [EQUIVALENT, 0 ms]
        (51) YES


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

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

   plus(0, x) -> x
   plus(s(x), y) -> s(plus(p(s(x)), y))
   times(0, y) -> 0
   times(s(x), y) -> plus(y, times(p(s(x)), y))
   exp(x, 0) -> s(0)
   exp(x, s(y)) -> times(x, exp(x, y))
   p(s(0)) -> 0
   p(s(s(x))) -> s(p(s(x)))
   tower(x, y) -> towerIter(x, y, s(0))
   towerIter(0, y, z) -> z
   towerIter(s(x), y, z) -> towerIter(p(s(x)), y, exp(y, z))

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:

   plus(0, x) -> x

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