Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270395

details
property	value
status	complete
benchmark	h16.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n136.star.cs.uiowa.edu
space	Hamana_Kikuchi_18
run statistics
property	value
solver	Wanda 2.1c
configuration	default
runtime (wallclock)	2.25276 seconds
cpu usage	2.24508
user time	2.17157
system time	0.073507
max virtual memory	148280.0
max residence set size	32284.0
stage attributes
key	value
starexec-result	YES
output
1.82/1.91	YES
2.22/2.24	We consider the system theBenchmark.
2.22/2.24	
2.22/2.24	  Alphabet:
2.22/2.24	
2.22/2.24	    0 : [] --> R 
2.22/2.24	    1 : [] --> R 
2.22/2.24	    cos : [] --> R -> R 
2.22/2.24	    d : [] --> (R -> R) -> R -> R 
2.22/2.24	    minus : [] --> R -> R 
2.22/2.24	    mul : [] --> R -> R -> R 
2.22/2.24	    pls : [] --> R -> R -> R 
2.22/2.24	    sin : [] --> R -> R 
2.22/2.24	
2.22/2.24	  Rules:
2.22/2.24	
2.22/2.24	    d (/\x.y) z => 0 
2.22/2.24	    d (/\x.x) y => 1 
2.22/2.24	    d (/\x.minus (f x)) y => minus (d (/\z.f z) y) 
2.22/2.24	    d (/\x.pls (f x) (g x)) y => pls (d (/\z.f z) y) (d (/\u.g u) y) 
2.22/2.24	    d (/\x.mul (f x) (g x)) y => pls (mul (d (/\z.f z) y) (g y)) (mul (f y) (d (/\u.g u) y)) 
2.22/2.24	    d (/\x.sin (f x)) y => mul (cos y) (d (/\z.f z) y) 
2.22/2.24	    d (/\x.cos (f x)) y => mul (minus (sin y)) (d (/\z.f z) y) 
2.22/2.24	    minus 0 => 0 
2.22/2.24	    mul 0 x => 0 
2.22/2.24	    mul x 0 => 0 
2.22/2.24	    pls 0 x => x 
2.22/2.24	
2.22/2.24	Using the transformations described in [Kop11], this system can be brought in a form without leading free variables in the left-hand side, and where the left-hand side of a variable is always a functional term or application headed by a functional term.
2.22/2.24	
2.22/2.24	We now transform the resulting AFS into an AFSM by replacing all free variables by meta-variables (with arity 0).  This leads to the following AFSM:
2.22/2.24	
2.22/2.24	  Alphabet:
2.22/2.24	
2.22/2.24	    0 : [] --> R 
2.22/2.24	    1 : [] --> R 
2.22/2.24	    cos : [R] --> R 
2.22/2.24	    d : [R -> R * R] --> R 
2.22/2.24	    minus : [R] --> R 
2.22/2.24	    mul : [R * R] --> R 
2.22/2.24	    pls : [R * R] --> R 
2.22/2.24	    sin : [R] --> R 
2.22/2.24	    ~AP1 : [R -> R * R] --> R 
2.22/2.24	
2.22/2.24	  Rules:
2.22/2.24	
2.22/2.24	    d(/\x.X, Y) => 0 
2.22/2.24	    d(/\x.x, X) => 1 
2.22/2.24	    d(/\x.minus(~AP1(F, x)), X) => minus(d(/\y.~AP1(F, y), X)) 
2.22/2.24	    d(/\x.pls(~AP1(F, x), ~AP1(G, x)), X) => pls(d(/\y.~AP1(F, y), X), d(/\z.~AP1(G, z), X)) 
2.22/2.24	    d(/\x.mul(~AP1(F, x), ~AP1(G, x)), X) => pls(mul(d(/\y.~AP1(F, y), X), ~AP1(G, X)), mul(~AP1(F, X), d(/\z.~AP1(G, z), X))) 
2.22/2.24	    d(/\x.sin(~AP1(F, x)), X) => mul(cos(X), d(/\y.~AP1(F, y), X)) 
2.22/2.24	    d(/\x.cos(~AP1(F, x)), X) => mul(minus(sin(X)), d(/\y.~AP1(F, y), X)) 
2.22/2.24	    minus(0) => 0 
2.22/2.24	    mul(0, X) => 0 
2.22/2.24	    mul(X, 0) => 0 
2.22/2.24	    pls(0, X) => X 
2.22/2.24	    d(/\x.minus(cos(x)), X) => minus(d(/\y.cos(y), X)) 
2.22/2.24	    d(/\x.minus(d(F, x)), X) => minus(d(/\y.d(F, y), X)) 
2.22/2.24	    d(/\x.minus(minus(x)), X) => minus(d(/\y.minus(y), X)) 
2.22/2.24	    d(/\x.minus(mul(X, x)), Y) => minus(d(/\y.mul(X, y), Y)) 
2.22/2.24	    d(/\x.minus(pls(X, x)), Y) => minus(d(/\y.pls(X, y), Y)) 
2.22/2.24	    d(/\x.minus(sin(x)), X) => minus(d(/\y.sin(y), X)) 
2.22/2.24	    d(/\x.pls(cos(x), ~AP1(F, x)), X) => pls(d(/\y.cos(y), X), d(/\z.~AP1(F, z), X)) 
2.22/2.24	    d(/\x.pls(d(F, x), ~AP1(G, x)), X) => pls(d(/\y.d(F, y), X), d(/\z.~AP1(G, z), X)) 
2.22/2.24	    d(/\x.pls(minus(x), ~AP1(F, x)), X) => pls(d(/\y.minus(y), X), d(/\z.~AP1(F, z), X)) 
2.22/2.24	    d(/\x.pls(mul(X, x), ~AP1(F, x)), Y) => pls(d(/\y.mul(X, y), Y), d(/\z.~AP1(F, z), Y)) 
2.22/2.24	    d(/\x.pls(pls(X, x), ~AP1(F, x)), Y) => pls(d(/\y.pls(X, y), Y), d(/\z.~AP1(F, z), Y)) 
2.22/2.24	    d(/\x.pls(sin(x), ~AP1(F, x)), X) => pls(d(/\y.sin(y), X), d(/\z.~AP1(F, z), X)) 
2.22/2.24	    d(/\x.pls(~AP1(F, x), cos(x)), X) => pls(d(/\y.~AP1(F, y), X), d(/\z.cos(z), X)) 
2.22/2.24	    d(/\x.pls(~AP1(F, x), d(G, x)), X) => pls(d(/\y.~AP1(F, y), X), d(/\z.d(G, z), X)) 
2.22/2.24	    d(/\x.pls(~AP1(F, x), minus(x)), X) => pls(d(/\y.~AP1(F, y), X), d(/\z.minus(z), X)) 
2.22/2.24	    d(/\x.pls(~AP1(F, x), mul(X, x)), Y) => pls(d(/\y.~AP1(F, y), Y), d(/\z.mul(X, z), Y)) 
2.22/2.24	    d(/\x.pls(~AP1(F, x), pls(X, x)), Y) => pls(d(/\y.~AP1(F, y), Y), d(/\z.pls(X, z), Y)) 
2.22/2.24	    d(/\x.pls(~AP1(F, x), sin(x)), X) => pls(d(/\y.~AP1(F, y), X), d(/\z.sin(z), X)) 
2.22/2.24	    d(/\x.mul(cos(x), ~AP1(F, x)), X) => pls(mul(d(/\y.cos(y), X), ~AP1(F, X)), mul(cos(X), d(/\z.~AP1(F, z), X))) 
2.22/2.24	    d(/\x.mul(d(F, x), ~AP1(G, x)), X) => pls(mul(d(/\y.d(F, y), X), ~AP1(G, X)), mul(d(F, X), d(/\z.~AP1(G, z), X))) 
2.22/2.24	    d(/\x.mul(minus(x), ~AP1(F, x)), X) => pls(mul(d(/\y.minus(y), X), ~AP1(F, X)), mul(minus(X), d(/\z.~AP1(F, z), X))) 
2.22/2.24	    d(/\x.mul(mul(X, x), ~AP1(F, x)), Y) => pls(mul(d(/\y.mul(X, y), Y), ~AP1(F, Y)), mul(mul(X, Y), d(/\z.~AP1(F, z), Y))) 
2.22/2.24	    d(/\x.mul(pls(X, x), ~AP1(F, x)), Y) => pls(mul(d(/\y.pls(X, y), Y), ~AP1(F, Y)), mul(pls(X, Y), d(/\z.~AP1(F, z), Y))) 
2.22/2.24	    d(/\x.mul(sin(x), ~AP1(F, x)), X) => pls(mul(d(/\y.sin(y), X), ~AP1(F, X)), mul(sin(X), d(/\z.~AP1(F, z), X))) 
2.22/2.24	    d(/\x.mul(~AP1(F, x), cos(x)), X) => pls(mul(d(/\y.~AP1(F, y), X), cos(X)), mul(~AP1(F, X), d(/\z.cos(z), X))) 
2.22/2.24	    d(/\x.mul(~AP1(F, x), d(G, x)), X) => pls(mul(d(/\y.~AP1(F, y), X), d(G, X)), mul(~AP1(F, X), d(/\z.d(G, z), X))) 
2.22/2.24	    d(/\x.mul(~AP1(F, x), minus(x)), X) => pls(mul(d(/\y.~AP1(F, y), X), minus(X)), mul(~AP1(F, X), d(/\z.minus(z), X))) 
2.22/2.24	    d(/\x.mul(~AP1(F, x), mul(X, x)), Y) => pls(mul(d(/\y.~AP1(F, y), Y), mul(X, Y)), mul(~AP1(F, Y), d(/\z.mul(X, z), Y))) 
2.22/2.24	    d(/\x.mul(~AP1(F, x), pls(X, x)), Y) => pls(mul(d(/\y.~AP1(F, y), Y), pls(X, Y)), mul(~AP1(F, Y), d(/\z.pls(X, z), Y))) 
2.22/2.24	    d(/\x.mul(~AP1(F, x), sin(x)), X) => pls(mul(d(/\y.~AP1(F, y), X), sin(X)), mul(~AP1(F, X), d(/\z.sin(z), X))) 
2.22/2.24	    d(/\x.sin(cos(x)), X) => mul(cos(X), d(/\y.cos(y), X)) 
2.22/2.24	    d(/\x.sin(d(F, x)), X) => mul(cos(X), d(/\y.d(F, y), X)) 
2.22/2.24	    d(/\x.sin(minus(x)), X) => mul(cos(X), d(/\y.minus(y), X)) 
2.22/2.24	    d(/\x.sin(mul(X, x)), Y) => mul(cos(Y), d(/\y.mul(X, y), Y)) 
2.22/2.24	    d(/\x.sin(pls(X, x)), Y) => mul(cos(Y), d(/\y.pls(X, y), Y)) 
2.22/2.24	    d(/\x.sin(sin(x)), X) => mul(cos(X), d(/\y.sin(y), X)) 
2.22/2.24	    d(/\x.cos(cos(x)), X) => mul(minus(sin(X)), d(/\y.cos(y), X)) 
2.22/2.24	    d(/\x.cos(d(F, x)), X) => mul(minus(sin(X)), d(/\y.d(F, y), X)) 
2.22/2.24	    d(/\x.cos(minus(x)), X) => mul(minus(sin(X)), d(/\y.minus(y), X)) 
2.22/2.24	    d(/\x.cos(mul(X, x)), Y) => mul(minus(sin(Y)), d(/\y.mul(X, y), Y)) 
2.22/2.24	    d(/\x.cos(pls(X, x)), Y) => mul(minus(sin(Y)), d(/\y.pls(X, y), Y)) 
2.22/2.24	    d(/\x.cos(sin(x)), X) => mul(minus(sin(X)), d(/\y.sin(y), X)) 
2.22/2.24	    d(/\x.pls(cos(x), cos(x)), X) => pls(d(/\y.cos(y), X), d(/\z.cos(z), X))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions all output return to Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10