Termination Proof Script

Consider the TRS R consisting of the rewrite rules


1:		f(y,f(x,f(a,x)))	→ f(f(f(a,x),f(x,a)),f(a,y))
2:		f(x,f(x,y))	→ f(f(f(x,a),a),a)

There are 7 dependency pairs:


3:		F(y,f(x,f(a,x)))	→ F(f(f(a,x),f(x,a)),f(a,y))
4:		F(y,f(x,f(a,x)))	→ F(f(a,x),f(x,a))
5:		F(y,f(x,f(a,x)))	→ F(x,a)
6:		F(y,f(x,f(a,x)))	→ F(a,y)
7:		F(x,f(x,y))	→ F(f(f(x,a),a),a)
8:		F(x,f(x,y))	→ F(f(x,a),a)
9:		F(x,f(x,y))	→ F(x,a)

The approximated dependency graph contains one SCC: {3,4,6}.

Consider the SCC {3,4,6}. The constraints could not be solved.

Tyrolean Termination Tool (0.02 seconds) --- May 4, 2006