Integ TRS Inner 43557 pair #381740639

details

property	value
status	complete
benchmark	18.itrs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n191.star.cs.uiowa.edu
space	Mixed_ITRS_2014

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.8632619381 seconds
cpu usage	7.714462154
max memory	5.80345856E8

stage attributes

key	value
output-size	121870
starexec-result	YES

output

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


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YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.itrs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given ITRS could be proven:

(0) ITRS
(1) ITRStoIDPProof [EQUIVALENT, 0 ms]
(2) IDP
(3) UsableRulesProof [EQUIVALENT, 0 ms]
(4) IDP
(5) IDPNonInfProof [SOUND, 369 ms]
(6) AND
    (7) IDP
        (8) IDPNonInfProof [SOUND, 129 ms]
        (9) IDP
        (10) IDependencyGraphProof [EQUIVALENT, 0 ms]
        (11) IDP
        (12) IDPNonInfProof [SOUND, 43 ms]
        (13) AND
            (14) IDP
                (15) IDependencyGraphProof [EQUIVALENT, 0 ms]
                (16) IDP
                (17) IDPNonInfProof [SOUND, 17 ms]
                (18) IDP
                (19) IDependencyGraphProof [EQUIVALENT, 0 ms]
                (20) TRUE
            (21) IDP
                (22) IDPNonInfProof [SOUND, 18 ms]
                (23) IDP
                (24) IDependencyGraphProof [EQUIVALENT, 0 ms]
                (25) TRUE
    (26) IDP
        (27) IDependencyGraphProof [EQUIVALENT, 0 ms]
        (28) TRUE


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(0)
Obligation:
ITRS problem:

The following function symbols are pre-defined:
<<<
 & 	~ 	Bwand: (Integer, Integer) -> Integer
 >= 	~ 	Ge: (Integer, Integer) -> Boolean
 | 	~ 	Bwor: (Integer, Integer) -> Integer
 / 	~ 	Div: (Integer, Integer) -> Integer
 != 	~ 	Neq: (Integer, Integer) -> Boolean
 && 	~ 	Land: (Boolean, Boolean) -> Boolean
 ! 	~ 	Lnot: (Boolean) -> Boolean
 = 	~ 	Eq: (Integer, Integer) -> Boolean
 <= 	~ 	Le: (Integer, Integer) -> Boolean
 ^ 	~ 	Bwxor: (Integer, Integer) -> Integer
 % 	~ 	Mod: (Integer, Integer) -> Integer
 > 	~ 	Gt: (Integer, Integer) -> Boolean
 + 	~ 	Add: (Integer, Integer) -> Integer
 -1 	~ 	UnaryMinus: (Integer) -> Integer
 < 	~ 	Lt: (Integer, Integer) -> Boolean
 || 	~ 	Lor: (Boolean, Boolean) -> Boolean
 - 	~ 	Sub: (Integer, Integer) -> Integer
 ~ 	~ 	Bwnot: (Integer) -> Integer
 * 	~ 	Mul: (Integer, Integer) -> Integer
>>>

The TRS R consists of the following rules:
eval(x, y) -> Cond_eval(x > 0, x, y)
Cond_eval(TRUE, x, y) -> eval(x - 1, y)
eval(x, y) -> Cond_eval1(y > 0 && x > 0, x, y)
Cond_eval1(TRUE, x, y) -> eval(x - 1, y)
eval(x, y) -> Cond_eval2(x > 0 && 0 >= x && y > 0, x, y)
Cond_eval2(TRUE, x, y) -> eval(x, y - 1)
eval(x, y) -> Cond_eval3(y > 0 && 0 >= x, x, y)
Cond_eval3(TRUE, x, y) -> eval(x, y - 1)
eval(x, y) -> Cond_eval4(x > 0 && 0 >= x && 0 >= y, x, y)
Cond_eval4(TRUE, x, y) -> eval(x, y)
eval(x, y) -> Cond_eval5(y > 0 && 0 >= x && 0 >= y, x, y)
Cond_eval5(TRUE, x, y) -> eval(x, y)
The set Q consists of the following terms:
eval(x0, x1)
Cond_eval(TRUE, x0, x1)
Cond_eval1(TRUE, x0, x1)
Cond_eval2(TRUE, x0, x1)
Cond_eval3(TRUE, x0, x1)
Cond_eval4(TRUE, x0, x1)
Cond_eval5(TRUE, x0, x1)

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(1) ITRStoIDPProof (EQUIVALENT)
Added dependency pairs
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